A tier list is a ranking of each character's metagame, based on tournament settings. It is an indicator of how each character is expected to perform, under tournament settings, in relation to the rest of the cast. Thus, tiers measure the potential of each character based on all currently known techniques and strategies that have been shown to be useful in tournaments. Tier lists are common in fighting games as well as many other competitive games involving a large selection of characters.
The tier list does not say anything about any single matchup. For example, if two players are equally matched in skill, and one uses Fox and the other uses Pichu, the tier list alone can not be used to predict the outcome of the match accurately. This is because the tier list looks at a character's overall potential and effectiveness, and individual matchups can be soft or hard counters that affect but do not entirely determine a character's ranking. For instance, in the aforementioned example, if the Fox vs. Pichu matchup was dramatically tipped in Pichu's favor, but Pichu suffered from poor matchups against every other character in the game, it would mean that Pichu beats Fox, but Pichu is still worse than Fox.
SSB tier list
This list is cited from a GameFAQs post and generally reflects the sentiments of top-level SSB players.
SSBM tier list
SSBB tier list
This is the first version of the tier list for Brawl. It was released on September 01, 2008, but like the other versions, is subject to change at any time.
Controversy of the Existence of Tiers
For a comprehensive detailing of the arguments in favor of the existence of tiers, see this page.
Controversy arises periodically over the existence of tiers, most notably during the "tier wars" at GameFAQs and Smashboards. Some smashers, called "anti-tiers," argue that every character can be played equally well. In support of this argument, they claim that the tier list creates a cycle in which players choose only higher-tiered characters, and thus only those characters develop an advanced metagame, thereby reinforcing the tier list.
The unanimous consensus of competitive players is that tiers do exist. They argue that it would be almost impossible to balance a game of unlike characters; without specific redesign, characters would have the tendency to fall into tiers by dint of their myriad variables (differing attack power, running speed, etc.). Furthermore, the developers cannot foresee top-level strategies, and thus even their deliberate efforts could fail to balance the game at a professional level. Years of empirical results support this conclusion as well; national tournament-winners of Melee almost always use Marth, Fox, Falco and Sheik.
The list itself is subject to change at any time. Optimal strategies for each character shift largely over time, changing the tier list as well. Anti-tiers use this point to argue that the tier list cannot be true if it changes. Pro-tiers respond by pointing out that it may be true for a particular, static metagame, and that this argument doesn't weigh against the existence of tiers themselves, but merely against a particular metagame.
Tiers exist at all levels of play, though the rankings are highly changed from casual play to competitive play, due to different strategies and a different metagame from the tournament level.