Here is a topdown example using box2d physics
Kartgame.rar is a demo where i've mapped the 3D co-ordinates to 2D (The 3D x,z values are mapped to Box2D x,y). The only drawback here is the track has to be flat (The steering is terrible, sorry 'bout that)
hotdog.rar is a game i recently made for the lowrez jam (I turned off the lowrez bit). It uses the simple kart physics but it also implements drift.
At line 216 and 224 of MoveVehicle.agc it calculates drift by taking the vector the car is traveling at and the vector of the force being applied to the car and lerps a value between those two.
You could easily check if the difference between those two values was too big and make the vehicle spin out (See gameplay.agc line 424)