I'll also mention some non-core races and non-core classes, but at least one core race for each class. I've assigned them not only out of game mechanics and powergaming, but also out of how I see the mindset of each race. This may vary from common stereotypes...
Adept (NPC) Human, halfling, orc, goblin
Aristocrat (NPC) Human, elf
Barbarian Half-orc, orc, human, halfling
Bard Human, half-elf, elf, halfling, gnome
Cleric Human, dwarf, gnome
Commoner (NPC) Human, halfling
Druid Gnome, halfling, elf, human
Expert Human, dwarf, halfling, goblin
Fighter Human, dwarf, hobgoblin, halfling, elf
Monk Human, gnome
Paladin Human, dwarf
Psion (Psi) Human, gnome
Psychic Warrior (Psi) Human, half-orc, orc
Ranger Elf, human, half-elf, gnome
Rogue Human, elf, halfling, half-elf, gnome, dwarf, goblin, kobold
Samurai (OA) Human, dwarf
Shaman (OA) Human, gnome, elf, half-elf
Shugenja (OA) Human, gnome, elf, half-elf
Sohei (OA) Human, dwarf
Sorcerer Human, halfling, kobold, hobgoblin
Warrior (NPC) Human, dwarf, hobgoblin, halfling, elf, orc, half-orc, half-elf
Wizard Human, gnome, halfling
Wu-Jen (OA) Human, gnome, elf