Breaking it Down!
If you break the Player's Handbook classes down into their component parts it might look something like this...
Warrior that relies on damage through strength (Barbarian rage)
Warrior that relies on soaking up hit point damage (Barbarian HD & DR)
Warrior that relies on high armor class (Fighter, Paladin)
Warrior that relies on fancy training (Fighter feats)
Warrior that relies on archery (Barbarian, Fighter, Ranger, Paladin)
Warrior with skills (Barbarian, Ranger)
Semi-warrior that relies on non-weapon combat (Monk)
Warriors that rely on extra attacks per round (Monk, Fighter, Ranger)
Master of knowledge (Bard)
Musical inspiration of allies (Bard)
Stealing (Bard, Rogue)
Sneaking (Bard, Ranger, Rogue)
Spellcasting, spontaneous (Bard, Sorcerer)
Spellcasting, memorized (Cleric, Druid, Wizard, Paladin, Ranger)
Healing (Cleric, Druid, Paladin)
Defeating undead (Cleric, Paladin)
Religious devotion (Cleric, Druid, Paladin, and maybe Ranger)
Animal friends (Druid, Ranger)
Shapeshifting (Druid)
Wilderness stuff (Druid, Ranger)
Fast movement (Monk)
Internal alchemy, or mystic body enhancement (Monk)
Pillar of good (Paladin)
Good saving throws (Monk, Paladin)
Mounted combat (Paladin, Fighter)
Killing evil (Paladin, Cleric)
Favored enemies (Ranger)
Assassination (Rogue sneak attack)
Trapfinding (Rogue)
Social skills (Rogue, Bard)
Combat maneuverability, mostly for flanking (Rogue, Monk)
Lots of spells per day (Sorcerer)
Variety in spell choices (Cleric)
Powerful and flexible spell choice (Wizard)
Lots of skill points to spend (Rogue, Bard, Ranger)
As we see, some concepts are tied to other concepts when players might only want part of the package and not the whole deal.
Many combinations haven't been tried recently. Spontaneously magic fighters or clerics with skill points like learned european monks or archers that aren't equally good with swords.