Warforged + Barbarian: ROBOBARBARIAN SMASH YOU
Pixie + Artificer: Everything you create is made out of sticks and twine.
Gnome + Swordmage: Play it up like you're a leprechaun. Every time the enemy tries to get away from you, you're teleporting up to them again with your dorky little hat throwing gold everywhere.
Revenant + Paladin: Nobody told you that duty ends with death.
Eladrin + Vampire: :'( no more immortal Aryan fairylife for you, you are a vampire now
Goliath + Witch: Similar to a regular witch, but larger.
Halfling + Warlock: One day you just saw one too many fireworks shows above the village green and you fucking snapped.
Deva + Rogue: You have lived a thousand lives before this one; and in each life you have done nothing but steal shit. Somewhere in the world is your stash of 1,000 lifetimes' treasure, but you can't remember where...
Orc + Battlemind: You have no clue that you posess psychic powers; all you know is that you are STRONGEST ORC.
Shardmind + Ranger: A crystal formation in the forest that somehow came alive one day.
et cetera, et cetera... basically any class with Pixie or Warforged is going to be fun. And probably most things with Kobolds, Dragonborn, Satyrs, etc.
Warforged + Druid: It says that your wild shape can be anything you like. There's nowhere that it says you can't be a robot who wildshapes into a car.
Human + Beastmaster Ranger: You play as a talking wolf. Your companion is a human ranger who is too stupid to live without you, but at least he's handy with the twin scimitars.
Human + Protector Druid: You play as a talking copse of trees (see: Danny the Street). You have a browbeaten human whose job it is to summon you to whatever area you want to be in. Once you're there, you can in turn summon natural creatures that dwell within you.
Human + Berserker: When you rage, you change gender until the rage ends. (no wait, make that Dragonborn + Berserker...)
Human + Shaman: Your spirit companion is actually yourself from a parallel universe. Whenever you summon them they start bickering with you.
Human + Warlord: Pick only powers that grant bonuses and free attacks to your allies, never any that require you to attack yourself. You are an old man who does nothing but lecture his allies about how things were better back in the old days.