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, and therefore version 1.1.3 of the game. Character customization is not taken into account, and Mii Fighters are considered to have default height, weight, and special moves.
However, as balance changes have been introduced since this list's release, including one just two days afterward that included two entirely new characters, its relevancy and legitimacy are unclear.
Existence of tiers
It is a common opinion among new or casual players of a fighting game that all the characters in the series are equal and have the same amount of potential. 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 spectators is that tiers do exist. In reality, it would be almost impossible for developers to balance a game of unique characters, because the differing properties of each character produce a large number of variables that cannot be constantly monitored and modified on the spot for the purpose of perfect balance. Thus, developers may not be able to foresee top level strategies before their game's release date, and even deliberate efforts (i.e. updates to Smash 4 or other recent titles) will not perfectly balance a game at a professional level. Furthermore, Masahiro Sakurai did not solely intend for the Smash games to be played at high competitive levels under tournament rulesets, which are what tiers are based off of, and his idea of balancing may have been different from that of other competitive games.
Power rankings, such as the 2015 SSBMRank, have demonstrated that the best Smash players generally use high-tiered characters, with only a handful of outliers; even then, players such as Shroomed and Plup, who mained Dr. Mario and Samus respectively, eventually switched to a higher tier character (both using Sheik far more often), and were ranked higher than in the previous rankings, while players like Axe and aMSa, despite continuing to use their lower-tiered mains, have picked up one or several top tier secondary characters, and have fallen slightly in rank. In Melee, Armada is a prime example of a world-renowned player who had to pick up a stronger character in order to overcome his Peach's growing matchup issues against other top players like Hungrybox and Leffen, and not only began taking more sets off of them, but also rose to the number one spot in the 2015 SSBMRank. For Brawl, Vinnie switched from Mr. Game & Watch to Ice Climbers and immediately saw better results, eventually being ranked 9th in the 2014 SSBBRank, and most, if not all the players on said power rankings have a pocket Meta Knight if they do not main him. Despite being touted as the best Bowser Jr. player in the world, Tweek dropped him in favor of Cloud, who he perceived to be a better choice in becoming the best Smash 4 player, and following the switch, he has seen consistent top 8 placings in Shots Fired 2, Do or DI, and most notably Pound 2016. There is also a noticeable trend of Bayonetta players beginning to dominate local scenes when they could not do so at all with their previous main, to the point of some regions considering to or banning Bayonetta altogether despite very few (if any) major tournament wins. Main switches are far less common in Smash 64, due to the game only having 12 characters, less polarizing balance issues, and the fact that most of the top players can play nearly every character at the same level regardless, making twelve character battles common.
It is important to note that every smasher mentioned above has put in a greater or equal amount of effort into their lower-tiered characters compared to top players who main higher-tiered characters, and has single-handedly pushed their characters' metagames to around the same level. However, barring a breakthrough in new tech that is useful and reliable (as seen with aMSa's Yoshi and Axe's Pikachu in Melee), or updates in Smash 4 that positively affect a character's viability (such as Mewtwo since version 1.1.3), lower-tiered characters by themselves are generally too inconsistent to survive in the long run against other top players who use higher-tiered characters; occasionally, such as with Ness in Smash 64, there is even a chance that a character can drop significantly in the tier list as a result of being much less effective than initially perceived. Thus, there is an inclination to simply use better characters. Tier lists are deliberately ever changing to reflect individual character performances in tournament, and as a result, only a few characters will ever see significant shifts in placement, while the remaining characters will rarely shift from the general position they are in now.