The Tier System is a ranking of the player character classes for OGL d20 system (D&D 3rd, 3.5 and Pathfinder), devised by the mix/maxing nerds at Gamesologists Forums, that compares the relative power and versatility of the different character classes. After burning out the bump limit in the forums a few times over, it became clear that some classes are just useless, and some are wickedly broken. The Tiers aren't about what classes you should *always* pick, but rather making sure the player characters in the party are balanced so that nobody feels like a fifth wheel. With a party of a Druid, Wizard, Bard and Monk, you can tell that the Monk player is gonna have much less fun because she'll be overshadowed by the others.
Some classes can move up and down, either with variants (already mentioned above, with some serious min/maxing and munchkinism or, for Pathfinder, a class option. The original thread says that the "Truenamer" class is pretty broken (as in, not working as intended,) and usually ends up at Tier 6 or worse - unless it's min/maxed out the wazoo to be able to spam its abilities, in which case it rises to Tier 4. Even then, being in the same tier doesn't make two classes equal, just in the same range - the hexblade's clearly shittier than the ranger or barbarian, but it still ekes out a spot in Tier 4, and the samurai's better than its NPC class bros just by virtue of having class features, even if they suck. The tier list also assumes that all the players are about the same level of skill and at least sort of know what they're doing; a druid who prepares nothing but heal spells and charges into combat with a scimitar while never wildshaping is a lot worse than a samurai who's minmaxed Intimidate enough to make every enemy within 30 feet shit themselves as a swift action. Tier 3 classes are generally considered the ideal balance point, being versatile and powerful but not so much so they can't be challenged.
Since WotC very rarely supported non-core classes beyond their initial book and core classes had fundamental flaws or their most broken abilities were core, what books are usable doesn't really matter much for 3.x tiers. Bard is the main exception, as core only bards are pretty lame but they have a huge amount of unique splat support. Pathfinder is different here because it actually supported its non-core classes and many classes used talents selected from a list every few levels which are well suited for expansion in splat. This still rarely matters, but it means certain retardedly broken options pop up from time to time. This generally works out to "take this and you're tier 2" and more archetypes that fundamentally change the class being in a different tier (though 3.5 had some).
The following is copypasta, mostly because the forum threads for this keep burning out over at Gamesologists, but partially so that fa/tg/uys can still look down their noses at the math nerds at Brilliant-Gamesologists-dot-Com. "Pathfinder examples" and "TPP examples" sections were not in the original post and have been added for convenience.
Note that the tier lists measure general ability to get shit done, rather than pure, balls-out combat power. Some martial classes are unstoppable terrors in combat, but once the fight stops, they might as well go crack open a soda, while wizards and skillmonkeys generally continue to contribute all the time. In fact, that's half of tier 4; classes that are super good at one or two things, but suck ass at doing anything else. The list also takes a look at more of the mid-to-late-game potential of classes: an unoptimised druid isn't that much better than an unoptimised barbarian at level 1, but as they both level up the gap between them widens exponentially.
- Tier System for Classes discussion at Brilliant Gameologists
-  A discussion about tiers for 5E classes]
- /tg/ turns socialist and tries to fix the class tier system.
- Note: Entries in italics are classes that the original author was not versed in, but had heard a lot about; take their tier placement with a grain of salt.
Capable of doing absolutely everything, often better than classes that specialize in that thing. Often capable of solving encounters with a single mechanical ability and little thought from the player. Has world changing powers at high levels. These guys, if played with skill, can easily break a campaign and can be very hard to challenge without extreme DM fiat or plenty of house rules, especially if Tier 3s and below are in the party.
Has as much raw power as the Tier 1 classes, but can't pull off nearly as many tricks, and while the class itself is capable of anything, no one build can actually do nearly as much as the Tier 1 classes. Still potentially campaign smashers by using the right abilities, but at the same time are more predictable and can't always have the right tool for the job. If the Tier 1 classes are countries with 10,000 nuclear weapons in their arsenal, these guys are countries with 10 nukes. Still dangerous and easily world shattering, but not in quite so many ways. Note that the Tier 2 classes are often less flexible than Tier 3 classes... it's just that their incredible potential power overwhelms their lack in flexibility.
- Examples: Zceryll, "The Star Spawn" vestige), , , , sorcerer (
- Pathfinder Examples: Oracle, Summoner, Witch.
Capable of doing one thing quite well, while still being useful when that one thing is inappropriate, or capable of doing all things, but not as well as classes that specialize in that area. Occasionally has a mechanical ability that can solve an encounter, but this is relatively rare and easy to deal with. Can be game breaking only with specific intent to do so. Challenging such a character takes some thought from the DM, but isn't too difficult. Will outshine any Tier 5s in the party much of the time.
- Examples: Bard, , , , , , , , ranger ( ), ,
- Pathfinder Examples: Alchemist,Bloodrager Investigator, Inquisitor, Magus, Skald, Unchained Summoner, Warpriest, Vigilante (Spellcasting archetype), Sacred Servant Paladin , Eldritch Scoundrel Rogue, certain Monk archetype combinations.
- TPP Examples: All Path of War classes, Tactician , Vitalist, Aeigis, Soulknife (Augmented Blade or War Soul archetype), most Spheres of Power classes, Occultist. (In short, most TPP class worth using were built to fall into this tier.)
Capable of doing one thing quite well, but often useless when encounters require other areas of expertise, or capable of doing many things to a reasonable degree of competence without truly shining. Rarely has any abilities that can outright handle an encounter unless that encounter plays directly to the class's main strength. DMs may sometimes need to work to make sure Tier 4s can contribute to an encounter, as their abilities may sometimes leave them useless. Won't outshine anyone except Tier 6s except in specific circumstances that play to their strengths. Cannot compete effectively with Tier 1s that are played well.
- Examples: Adept, barbarian, fighter (Zhentarim soldier substitution levels), , , ranger, rogue, , , ,
- Pathfinder Examples: Paladin, Kineticist Cavalier, Slayer, Unchained Monk, certain Monk archetypes. , Vigilante , small sized
- TPP Examples: Soulknife (Psionics Unleashed).
Capable of doing only one thing, and not necessarily all that well, or so unfocused that they have trouble mastering anything, and in many types of encounters the character cannot contribute. In some cases, can do one thing very well, but that one thing is very often not needed. Has trouble shining in any encounter unless the encounter matches their strengths. DMs may have to work to avoid the player feeling that their character is worthless unless the entire party is Tier 4 and below. Characters in this tier will often feel like one trick ponies if they do well, or just feel like they have no tricks at all if they build the class poorly.
- Examples: Expert, fighter , , , monk, , paladin , (with feat), , ,
- Pathfinder Examples: Medium sized Cavalier, Gunslinger , Swashbuckler .
Not even capable of shining in their own area of expertise. DMs will need to work hard to make encounters that this sort of character can contribute in with their mechanical abilities. Will often feel worthless unless the character is seriously powergamed beyond belief, and even then won't be terribly impressive. Needs to fight enemies of lower than normal CR. Class is often completely unsynergized or with almost no abilities of merit. Avoid allowing PCs to play these characters.
- Examples: Aristocrat, commoner, , warrior
A class so terrible it gets its own tier, the "is just broken (as in, the class was improperly made and doesn't function appropriately). Highly optimized (to the point of being able to spam their abilities) a Truenamer would be around Tier 4, but with lower optimization it rapidly drops to Tier 6." They can however be optimized to do some very specific things that no other class can, with god killing mastery of cosmic power, while still being trumped by a couple of enthusiastic bandits.
Not in the original list but often mentioned is a "Tier 0". Tier 0 is unique in that it applies to builds, albeit broad ones, not base classes. The primary idea is that while Tier 1 still needs to select what spells he prepares ahead of time, Tier 0 can pull the needed ability out of his ass when he sees a problem. The classic example is the "Rainbow Warsnake", a Warmage (traditionally, but Dread Necromancer and Beguiler also work) that adds the entire Cleric list, core and splat, to his spell list by taking 10 levels of Rainbow Servant. Since for a Warmage his "spell list is the same as his spells known list" he can just cast any spell on the Cleric list spontaneously to deal with problems as they come up.
Pathfinder briefly had Tier 0 Sorcerer and Oracle via the spell Paragon Surge. Paragon Surge grants the user a feat, chosen when the spell is cast. This feat could be spent on Expanded Arcana, which gave you an extra spell known of your highest level or two of a lower level. This meant a Sorcerer or Oracle could known any on list spell the player wanted to at the cost of a standard action and third level spell slot (or swift and 7th/metamagic rod and 3rd). This naturally got nerfed and now any future castings the same day give you the same feat. Still potent, and possibly enough to make the gap to tier 1, but not as stupidly broken.
Potentially still Tier 0 in Pathfinder is the Sorcerer archetype Razmiran Priest. This archetype is capable of casting single use magic items of divine spells without expending them by blowing their own spell slots. This allows them to get as wide a spell list as an Archivist, able to cast any divine spell they have a scroll or 1 charge wand of, but cast each spell whenever they want. This requires a Use Magic Device check, but it's piss easy to get it to the point you pass even on a roll of 1. This archetype is generally kept in check by its fluff, which requires being mutated by a crazy evil wizard pretending to be a god.
The original tier system did not assume prestige classes, assuming all classes got the same level of optimization and a took a straight 20 levels anyways. This left a gap to be filled and so a second type of tier system was created for prestige classes. This system rates prestige classes based on how much more or less powerful they are than their "logical entry", a base class or combination of them that is the most logical and quickest way to enter a prestige class. For example: A prestige class that required casting second level arcane spells could be entered as a Wizard 1 by taking the Precocious Apprentice feat (an infamous way to enter such classes early), or Ranger 5/Assassin 3 (a late and terrible choice) but will typically be entered by three levels in Wizard.
- +2: Really strong. The most broken cheese (Ur-Priest's double speed Cleric casting) is here. This also includes prestige classes that are not broken but are most logically entered by a terrible base class (Soulknife going into Soulbow). Often enough to raise a class a tier on the original system.
- +1: A notable increase in power, but not serious.
- +0: A sidegrade or incredibly minor power boost.
- -1: Like +1 but reversed.
- -2: These tend to be absolutely unsalvageable prestige classes. Often just plain old don't work or are extremely hard to enter by poor design.
While the idea was well received and the system is known to 3.X optimizers, this system never got all that popular compared to its parent system.