What are tiers?
Tiers are a ranking of how "powerful and/or versatile" the various 3.5 base classes are, with low numbered tiers being considered more capable than high numbered tiers. It's important to remember that certain caveats apply to the rankings:
- Tiers assume similar levels of optimization. Someone playing an optimized "weak" class (like a fighter) and using its abilities well may be a lot more effective than a poorly built wizard played by someone who doesn't know how to make use of its options.
- Tiers attempt to describe power over levels 1-20. Classes will generally be in their listed tiers immediately, though the gaps between tiers tend to be a bit smaller at lower levels.
- Tiers are based on published material only. Homebrew and house rules can and will modify the rankings of some classes or even just negate the entire ranking system.
- Tiers are based on relatively high-magic games, as presented as the default in the core rulebooks. In a low-magic setting the rankings will be mostly the same, but the gaps between tiers will get a lot bigger, because magic items tend to be the best way for less powerful classes to cover up their weak spots.
- Tiers look at characters' ability to solve problems of any sort, not just combat (social challenges, exploration, dungeon navigation, and other challenges presented in published adventures or suggested in the game texts to the DM).
We frown on link-only answers, so I'll go ahead and summarize the full tier list of all published classes, originally from here. Fuller descriptions of why each class is in its tier can be found here.
Wizard, Cleric, Druid, Archivist, Artificer, Erudite (Spell to Power variant) — Can do anything and everything, often better than lower-tier classes that supposedly specialize in that thing.
Sorcerer, Favored Soul, Psion, Binder (w/ online vestiges), Erudite — As powerful as tier 1, but no one build can do everything.
Beguiler, Dread Necromancer, Crusader, Bard, Swordsage, Binder, Ranger (Wildshape variant), Duskblade, Factotum, Warblade, Psychic Warrior, Incarnate, Totemist — Good at one thing & useful outside that, or moderately useful at most things.
Rogue, Barbarian, Warlock, Warmage, Scout, Ranger, Hexblade, Adept, Spellthief, Marshal, Fighter (Zhentarium variant) — Good at one thing but useless at everything else, or mediocre at many things.
Fighter, Monk, Ninja (both CA & Rokugan versions), Healer, Swashbuckler, Soulknife, Expert, OA Samurai, Paladin, Knight, CW Samurai (with Imperious Command), Soulborn — Good at one rarely applicable thing, or mediocre at one thing, or simply too unfocused.
CW Samurai, Aristocrat, Warrior, Commoner — Objectively worse at their specialty than another (often Tier 5) class, without anything else to show for it.
Truenamer — Apparently received no actual playtesting, mechanics as written simply don't work. See this question for more details.