Down Air Attack

Lucario dair — Lucario's down aerial, which negates momentum.

The down aerial (abbreviated as "dair", "DAir", "d-air" or "ADA") is an aerial attack that is performed in midair by pressing the A Button, and tilting the control stick downwards. Its official term varies between titles, where it is known as a "Down Midair Attack" in Super Smash Bros. Melee, and a "Down Air Attack" in Brawl. Many of these moves are Meteor Smashes.

List of Down-airs in Super Smash Bros.

Down airs in SSB either are one of three things: drills, spikes, or just sideways knockback-oriented moves. Due to most of them being drills, they are some of the few moves that can be easily DI'd out of in an otherwise low DI game.

Captain Falcon: A powerful spike. Can also combine a down air into Falcon punch at mid or high percents depending on character.
DK: High power spike. Too little range. Combos well into both up smash, aerials, and Giant Punch at varying percentages.
Fox: A very fast drill. Easy to DI out of. Combos into up smash, shine, and tap a combos.
Jigglypuff: Similar to the other drill based characters, combos into up tilts and up b.
Kirby: A drill that is very difficult to DI of, very useful in both combos and gimping. Considered by many the best gimping move in all of SSB64. Down air on the ground combos into up tilts and f-smashes. Really good vs shields as well.
Link: Very useful move to short hop. Has the most ending lag of any aerial and is overall the best way of showing the difference of Not Z-cancelling and Z-cancelling. Great power and great vs shields if Z-cancelled.
Luigi: A drill so its easy to DI out of. A good combo move and good vs shields. Can combo a down air into up b or down air into up air into up b. If there wasn't smash DI in ssb64, this move would be Luigi's best move.
Mario: Similar to Luigi but slightly more useful. combos into up air. A drill but with quicker hits so it is more difficult to DI out of. Good vs shields as well. Part of the basic Short hop down air short hop up air combo.
Pikachu: A high priority move like Pikachu's other aerials. Great shield stun.
Samus: High power and priority spike. Usually considered Samus's best move. Main kill combo is Down air into back air or charge shot. You can also repeatedly down air opponents and anticipate techs. Short hop down airs can lead to shield break if the opponent is careless.
Yoshi: The most damaging move in SSB64 if all moves hit. Shield breaker. It is however a drill so its easy to DI out of. If the opponent can't DI well, a very easy 0 to death is up tilt into down air repeated. Weakest DJC aerial but good to combo into F-smash.

List of Down Airs in Super Smash Bros. Melee

Mario: Performs a drill kick. Is somewhat functionally identical to his Mario Tornado (in fact dealing the same amount of damage), but strikes faster, is harder to escape from, and has no finishing punch, making it a good damage-racker and having good combo potential. The drill will usually carry enemies with him, so it can be used in a similar manner to his SSB down air by using it repeatedly as a psuedo-Meteor Smash and then using the Mario Tornado and Super Jump Punch for recovery.
DK: Stomps the air below him. Will powerfully Meteor Smash his foe.
Yoshi: Kicks his legs very rapidly below him. Can deal at least 40% damage if performed correctly. It weakly Meteor Smashes.
Peach: Kicks below herself. Good combo starter.
Bowser: Spins upside-down in his shell. Can be used in a somewhat similar fashion to Mario's due to the multiple quick hits, though the landing lag is comparatively larger.
Samus: Swings her arm below her. Is usually a fairly powerful Meteor Smash, but is a tad slow.
Link: Thrusts his sword below him. It is a powerful attack, and will knock his foe at an upwards angle. It is very easy to Star KO with this attack, however, the landing lag is incredibly long.
Zelda: Sticks her leg out below her. Has a very small sweetspot, but if it hits, her foe will be Meteor Smashed.
Sheik: Points her leg out and falls at a downwards angle. Knocks her foe very slightly horizontally.
C. Falcon: Thrusts his legs below him. Another powerful Meteor Smash. If the attack connects in the upper hitbox, the attack becomes even more powerful and unable to be Meteor Canceled.
Fox: Performs a drill kick. Another Mario-esque Down Air Attack, useful for generally the same purposes. However, this attack very weakly Meteor Smashes an opponent.
Kirby: Performs a drill kick. It induces a weak Meteor Smash on his foe.
Pikachu: Turns upside down and spins around emitting electricity from its cheeks. Another simple drill move, though it suffers from slight landing lag.
Ness: Smashes the air below him with his foot. It will Meteor Smash his opponent.
Ice Climbers: Place their hammers below them, and drop down. Knocks the enemy a fair distance upwards.
Marth: Slashes his sword downward. If the tip of the sword hits, a powerful Meteor Smash is executed.
Luigi: Spins around, performing a downwards kick. Appears identical to Mario's, but instead of multiple, low knockback hits, he performs one quick spin that can knock the enemy in diverse directions. If Luigi hits his foe with his spinning fists or hip during the start of the attack, they will be powerfully Meteor Smashed, though strangely, if a match is cleared and the attack doesn't contact the foe with hip or fists, he or she is still considered to have been Meteor Smashed at the results screen. Mario's Mario Tornado bears a similar property, despite the fact that it doesn't send the enemy downward at all.
Jigglypuff: Performs a drill kick identical to Kirby's, but will not Meteor Smash its foe. However, it can semi-spike.
Mewtwo: Backflips and kicks downwards. Another Meteor Smashing attack.
Mr. Game & Watch: Pulls a key out and plunges downward. If it hits immediately at the start of the attack, Mr. Game & Watch will Meteor Smash his foe.
Dr. Mario: Same as Mario's, dealing seven, multiple hits although the sound effect is different.
Falco: Identical to Fox's, but will instead spike his foe since the opponent cannot cancel the hitstun. It is quite possibly the easiest spike to perform in the game, but Falco falls quite fast while executing the attack.
Pichu: Identical to Pikachu's, but if it hits the ground, Pichu will receive 1% damage.
Young Link: It is identical to Link's, but it Meteor Smashes if the opponent is above or to the side of him.
Roy: Identical to Marth's, but the sweetspot required to Meteor Smash is located a bit higher.
Ganondorf: Identical to Captain Falcon's, but comes out slower and is more powerful.

List of Down-airs in Super Smash Bros. Brawl

Mario: The famous Mario Tornado, replaced by the F.L.U.D.D. as a down special, is now his dair. Outer hitboxes draw the opponent into the center.
Luigi: Spins rapidly in place. Multiple effect-varying hitboxes surrounding feet, arms, and torso. If the arms connect, it becomes a strong Meteor Smash.
Peach: Thrusts legs rapidly below herself at a slight angle. Good for starting combos.
Bowser: Flips upside-down and rotates around inside his shell. Racks a lot of damage, and has an additional hit upon landing, which helps to keep opponents from taking advantage of the large landing lag.
Donkey Kong: Thrusts leg below him to always Meteor Smash very powerfully while performing a strong-man pose in midair.
Diddy Kong: Clasps one hand over the other. Extremely powerful Meteor Smash and can star KO.
Yoshi: The greatest damage racking aerial in the game. Flutter kicks very fast below him. Deals 33% and Meteor Smashes after last hit.
Wario: Flips upside down and rotates once or twice. When the move connects, he makes contact up to 7 times. Great damage racker.
Link: Kneels above his sword with it upside down. Extremely powerful, incredibly long duration, and no startup lag. There is noticeable ending lag though, when he lands on the ground and has to yank it out. Also, if he hits an opponent, Link will hop up in the air (unless Link is fastfalling).
Zelda: Thrusts leg once below her vertically. Meteor Smash if sweetspotted, but it becomes much weaker if not sweetspotted.
Sheik: A Stall-Then-Fall. Sheik bends her body behind her center of gravity and leans leg out below her. Minimal knockback, and is dangerous to use, but it is very slow.
Ganondorf: Jams legs underneath him. Multiple hitboxes, having weaker base knockback in the body than in his legs but by far the highest knockback scale in the game and always Meteor Smashes if it connects. It is the most powerful Meteor Smash in the game at 38% or higher and the 3rd strongest at 0% with OHKO potential - in fact, if it hits a grounded opponent, they can bounce off the ground and be Star KO'd at percents as low as 80% against light characters. Has an electric effect.
Toon Link: An incredible priority Stall-Then-Fall. Similar to Link's, although rockets downwards, stopping only when used in very high altitudes, and can Meteor Smash near beginning few frames. Dangerous to use when not above ground, but if you have more lives than foe, risk one to spike them as they recover. Like Link's, it bounces off the opponent; after the bounce, it works like a normal aerial attack.
Samus: Flips 90 degrees forward and faces the screen while swinging arm cannon in a 180 degree arc below her. It is a Meteor Smash, but is also quite slow.
Zero Suit Samus: A Stall-Then-Fall. Turns body in a linear form, then propels downward. If foe is hit in the air, they are carried down until they are knocked away once in contact with ground. Might make food for thought about "Zerocide" if it is used on a foe in the air and is carried downwards until both ZSS and foe KO. This move, because of its knockback, Meteor Smashes.
Pit: Swings both halves of bow downwards. This move incurs upwards knockback most of the time.
Pit: A half Stall-Then-Fall. Both position hammers below themselves and fall downwards a very slight distance. Knockback is upwards and a bit diagonal.
R.O.B.: Pauses momentarily, then blasts boosters powerfully downwards. Will Meteor Smash if hits. Can be used to stop vertical momentum, but is hard to use correctly, and will propel a bit upwards if incorrectly used.

Spike — Some down aerial attacks spike the opponent.

Kirby: Spins around in multiple circles. Legs produce most damage and knockback. Can Meteor Smash.
Meta Knight: Swings sword below him. Similar to Marth's Down Aerial, but will Semi-Spike instead of Meteor Smashing. Can be used on the ground (short-hopped) to set up a kill by edgeguarding. Very safe move.
King Dedede: Spins hammer around under him for multiple hits. Works well in the ascent of a ground jump.
Olimar: Arcs a Pikmin below his knees. Similar to bair and fair. If the enemy is directly below Olimar, it becomes a Meteor Smash, with power varying by Pikmin - purple, yellow, and red are very strong, blue is of mediocre strength, and white is weak.
Fox: Spins legs around, a bit diagonally, hitting multiple times. Weakest Meteor Smash in the game after last hit. Similar to Falco, Kirby, or Jigglypuff's dairs. Useful when shorthopped for combos.
Falco: Same as Fox's, except only one hit, not several. No lag, and strong Meteor Smash when hit near first to near-last frames and hit in the middle to bottom hitbox of his body. Has a disjointed hitbox.
Wolf: Similar to Diddy Kong's. Laggier, though it connects more often because of Wolf's much faster air speed compared to Diddy Kong.
Captain Falcon: Same as Ganondorf's, except quicker, and doesn't Meteor Smash as powerfully. Can no longer Nipple Spike, unlike in Melee.
Pikachu: Like his Forward aerial, but downwards with only one hit. High lag when landing.
Squirtle: Similar to Mario Tornado, but is better vertically ranged because of Squirtle's long tail.
Ivysaur: Blasts its bulb below himself. Surprisingly, does not launch Ivysaur upwards, but stalls it in the air, like Lucario's Down Aerial. Can be a powerful Meteor Smash if the foe is right beneath Ivysaur, but it's laggy and not so useful due to Ivysaur's extreme vulnerability to edge hogs when it is off stage.
Charizard: Flicks tail out of hitboxes and stomps his feet down. Very strong, and Meteor smashes. Sends grounded opponents upwards and sideways.
Lucario: Blows up two bursts of aura beneath its foot. Stalls all frames of vertical momentum and can be used to delay it. Very powerful move in general and can be used in multiple ways because of immobility.
Jigglypuff: Spins around. Identical to Kirby's. Almost no knockback unless at percentages above 200%. Can lead to a Rest
Marth: Swings sword beneath his legs. Can Meteor Smash if hit at any part of the tip, but has some poor landing lag and ending lag in Brawl.
Ike: Faces screen while swinging sword down. If hits during initial frames, it Meteor smashes. Harder to use as a Meteor Smash than most because of the poor horizontal range. One of Ike's four spikes.
Ness: Jams foot down. Somewhat laggy, but is an extremely powerful Meteor Smash (2nd strongest meteor smash at 0%). It has diagonal knockback if the move connects in later frames.
Lucas: Four quick downward kicks. Can rack up to 20% damage, each kick doing exactly 5%. A medium power Meteor Smash served with last kick. Can be used easily to hit an Edge-hogging opponent.
Mr. Game & Watch: A Stall-Then-Fall (Donkey Kong Jr.), Grabs a key and plunges downwards. Upwards knockback; similar in most ways to Ice Climbers' stall then fall. Can be aimed slightly to the side and can be canceled in the middle with Fire. Can also perform the Stall-Then-Fall Glitch along with Toon Link. Is a Meteor Smash if the enemy is directly under him and during initial frames, and if you tap down on the d-pad after executed, the move will slow. Much less risky Stall-Then-Fall than other ones.
Snake: Launches four subsequent kicks below himself. Similar to Lucas', but more damage, knockback, and doesn't Meteor Smash. Can be used very well in a short hop for a medium-high percent kill on a grounded opponent. Similar to his neutral aerial, this can do up to 28% damage having the last stomp higher knockback than his neutral aerial and last hit being able to connect in a short hop at the expense of being harder to trap with.
Sonic: A Stall-Then-Fall. Lasts a long duration, but has high landing lag. After some frames, this move can be cancelled with his Spring Jump.

Notable characters' down aerials

Captain Falcon's down aerial, notorious for the nipple spike in Melee.
Falco Lombardi's down aerial, a fast spike in Melee and Brawl with high range vital to Falco's pillar.
Fox McCloud's down aerial, notorious for its use in his infinite combo.
Wolf's down aerial, a spike exact in strength to Falco's Dair spike, although it takes a split second longer to complete.
Lucario, Ivysaur, R.O.B.'s down aerials all stop vertical momentum, making those moves good for recovery.
Mario's down aerial was replaced as the Mario Tornado in Brawl. Before, Mario Tornado used to be his Down Special Move.
Yoshi's down aerial, a very damaging move which can rack up to 40% with its multiple kicks.
The Ice Climbers, Mr. Game & Watch, Sheik, Sonic, Toon Link and Zero Suit Samus' down aerials, all of which are Stall-Then-Fall aerials in Brawl. Also, if Toon Link's down aerial hits a foe, he will "pogo-hop" and allow him to hit another enemy again.
Ganondorf's down aerial in Brawl can be auto canceled in short hops and KO below 100% who connects on the ground while in an aerial opponent making it a great approach move and as a spike it always spikes if connects with enough power to OHKO an opponent in most cases.
Marth's down aerial, possibly the most feared with its speed, range, and ability to spike in both Melee and Brawl.

Notes

According to the SSBB Prima Official Game Guide, Wolf's Down Aerial Attack is a "Dair" spike, and is indeed similar to Falco's "Dair" spike.