In gaming, a tier list is a list that ranks all characters based on the strength of their fighting abilities and their potential to win matches under tournament conditions, assuming equal skill on the part of each player. A tier list is decided based on the analysis of the following:
Tier lists are commonly made for fighting games that are played on the high competitive level, such as Mortal Kombat 9. Some games that aren't fighting games, but have large character sets, such as the Pokémon series, can also have their own tier lists.
The metagame of each game in the Super Smash Bros. series encompasses all the currently known techniques and strategies that have proven useful during tournament matches, thus, the tier list for each game ranks and measures the expected competitive performance of every character, based upon analysis of these techniques and strategies. The most widely accepted tier lists in the English-speaking community are those produced by the Smash Back Room on Smashboards; the first tier list for Super Smash Bros., however, was produced by GameFAQs.
Individual matchups affect, but do not ultimately determine, characters' tier list rankings. Often, a particular character will carry a supposed advantage over another character — such a matchup is known as a counter. However, some characters have an advantage over a character that is higher on the tier list. For example, in Super Smash Bros. Brawl, Peach holds an advantageous matchup against the Ice Climbers, but suffers from matchups poorer than the Ice Climbers' against nearly every other character in Brawl. While she can be considered a counter to the Ice Climbers, Peach is still ranked lower than the Ice Climbers on the tier list (due to poorer overall matchups, among other reasons). Thus, if two players at the top of the known metagame played a match with Peach and the Ice Climbers, the tier list alone could not predict the outcome of the match. Furthermore, tier lists do not rank characters relative to the numerical average of their matchup scores.
How much matchups affect a character's ranking is mostly on how well they perform against the more common characters in tournaments. For the most extreme example, in Brawl, a character's matchup against Meta Knight is a major part of their ranking, as Meta Knight is so ubiquitous in Brawl tournaments that a character cannot feasibly perform well if they are significantly countered by him. As a result, many characters, such as R.O.B., Pit, and Ike, perform noticeably worse in competitive play and suffer a significant drop on the tier list because of their inability to effectively fight Meta Knight. Other characters get boosted by their effectiveness at fighting top/high tier characters, such as Wolf, who despite having a few notable counters, is ranked rather highly in large part because his ability to go even or near even against the entire top tier and several high tier characters. On the other hand, performing especially well against lower tier characters has much lower impact on a character's competitive success and tier position. The most prominent example, King Dedede, harshly counters many borderline and lower tier characters, even moreso than top and high tier characters do besides Meta Knight. However, Dedede is in return countered by many of the top and high tier characters in Brawl (including the aforementioned Meta Knight), the characters he'll play against much more often in tournaments, thus preventing him from doing as well in tournaments as the top/high tier characters do, resulting in a lower tier ranking.
Super Smash Bros. tier list
The following is the Super Smash Bros. tier list produced by the 64 community. The numbers below the characters are their average ranking during the voting for the tier list. It is current as of May 12, 2015. 
Super Smash Bros. Melee tier list
The following is the twelfth Super Smash Bros. Melee tier list, which is also the first list to not be produced by the Smash Back Room, but rather by fan votes and feedback. It is current as of December 10th, 2015. 
Super Smash Bros. Brawl tier list
Super Smash Bros. 4 tier list
The following is the first Super Smash Bros. 4 tier list produced by the Smash Back Room. It is current as of February 1st, 2016. However, the relevancy of this tier list is unclear due to the release of patch 1.1.4 on February 3rd, 2016. Character customization is not taken into account, and Mii Fighters are considered to be at default height, weight, and special moves. The fighters Corrin and Bayonetta are not included on the current list due to them being released 2 days after the tier list's initial release.
Controversy over the existence of tiers
It is a common opinion among some players (mostly new ones) that all the characters in the series are equal. These players believe that the inherent strengths and weaknesses of characters balance them out, thus eliminating the need for tiers. However, the consensus of competitive players, and knowledgeable but non-competitive players, is that tiers do exist. They argue that it would be almost impossible for developers to balance a game of unlike characters, because the differing properties of each character produce a large number of variables that cannot successfully be monitored and modified for the purpose of perfect balance. Thus, developers may not be able to foresee top level strategies, and even deliberate efforts will not perfectly balance a game at a professional level. Furthermore, the developers did not solely intend for games in the Smash series to be played at high competitive levels under tournament rulesets, which are what tiers are based off of, and their idea of balancing may have been different from that of other competitive games.
Years of results from tournaments also support the existence of tiers: national tournament winners of Melee have most commonly used Marth, Jigglypuff, Fox, Falco, and/or Sheik, winners of Brawl nationals have most commonly used Meta Knight, Ice Climbers, Olimar, Snake, Diddy Kong, and/or Falco, and winners of Smash 4 nationals commonly use Sheik. Power rankings for the games have also demonstrated that the best Smash players generally use high-tiered characters. The top 25 players on the SSBPD for Melee was almost entirely composed of smashers who used top- or high-tier characters; the sole two exceptions were Shroomed, who used Dr. Mario (then considered a middle tier character), and Axe, who used Pikachu (then considered a low-mid tier character), and even these two players had top-tiered secondaries, with the former using Sheik and Marth and the latter using Fox and Falco. The later 2013 SSBM Player Rankings and 2014 SSBM Player Rankings showcased a similar trend to the SSBPD, with the top 25 players on both rankings primarily featuring smashers dedicated to top-tiered characters. Collectively between the two lists' top 25 places, only four players used characters not found in Melee's S tier: the aforementioned Axe and Shroomed, as well as Plup and aMSa, the latter two of whom were added in the 2014 rankings.
Controversy periodically arises over the existence of tiers, most notably during the "tier wars" on GameFAQs and SmashBoards. Some smashers, called "anti-tiers", argue that every character can be played equally well and that therefore, tiers do not exist and tier lists are unnecessary. To support this argument, they claim that the presentation of a tier list creates a cycle in which players see the list, and choose only higher-tiered characters to compete with, which causes only those characters develop an advanced metagame, thereby reinforcing the high-tiered characters' positions. They also argue that the tier list cannot be true because it continuously changes. The problem with the former argument, is that while higher tiered characters do see more usage, even the lowest ranked characters have professionals dedicated to using them, such as Taj and aMSa in Melee and Vermanubis and Boss in Brawl. These professionals put in as much effort and time, if not more, as the players of higher tiered characters to develop their characters' metagames, and continually discover advanced techniques of theirs. Despite this, barring a breakthrough discovery, the playerbase of lower tiered characters has routinely performed worse in tournaments than that of higher tiered characters, with even the best player of a lower tiered character very rarely ever placing high enough to win money in national tournaments without strong top-tiered secondaries. Additionally, while rare, there have been cases of a player dropping their main character for a higher tier character, and then performing even better in tournaments, such as Vinnie, who became one of the best players in the United States when he started using the Ice Climbers instead of Mr. Game & Watch. He has since seen much better results in the tournament scene, even on an international scale; Vinnie was later ranked as the 9th best Brawl player in the world in 2014. In response to the fact that the tier list changes, pro-tiers state that the anti-tiers' argument does not weigh against the existence of tiers, because the tier list must change as the metagame changes and new strategies previously unknown are discovered; while an individual tier list may not stay accurate forever, as explained in the previous paragraph, it does not discredit the existence of tiers.