As others have said, you don't need a perfect racial match (or even a primary score match) to work fine. We have a dragonborn assassin in my party who works it perfectly well, for example.
However there are certainly iconic combos that don't work as well as they probably should. There is also the pleasure of making a weird against-type combo that can be pretty fun (e.g. a dwarf cleric).
That said, iconic matches that aren't really supported by the rules:
Half-Elf Rangers and Rogues (especially Eberron Inquisitives)
Drow Wizards and Clerics
Tiefling Helllocks
Warforged Artificers
Dwarf Artificers
Halfing Druids/Shamans (Dark Sun), Clerics (Eberron) and Battleminds (pre-essentials)
Shadar-Kai Dark Pact Warlocks
Eladrin Bards/Feylocks/Telephatic Psions/Illusionists (pre-essentials)
Elf Sorcerers and Illusionist Wizards (pre-essentials)
Gnome Rogues
Deva Paladins and Runepriests
Goliath Seekers and Shamans
Half-Orc Battleminds
Kalashtar Monks, Psions, and Battleminds
I include Battleminds for Halfings and Half-Orcs, because if you read Psionic Power, they have a strong arrogance and iconoclastic feel, which IMHO is a nice match for both of those races.