I swap between kart combos all the time, many which are set, but here are the ones I most commonly stuck with
I really hate leaving out GLA, Circuit Special, Sports Coupe, Tanooki Kart, Jet Bike, Varmint, Flame Rider, Slick, and Super Glider out of this list though, since I love them both, just not as much as the aforementioned combo I use.
When in 150cc I choose various combinations, even though the main ones I tend to use are (in order of frequency)
In 200cc, I'm experimenting with various combinations, but I mainly tend to use two combinations:
If I want a bit of variety there's Wendy:
But let's not forget about the incredibly awesome (to look at) Yoshi on inside drifting bike, already celebrated in Mario Kart Wii:
The funny thing is that if you use an inside drifting bike, Yoshi makes an happy face while on a standstill (and, as a consequence, before the race starts), whereas if you give him an ATV or an outside drifting bike, he keeps his mouth shut: http://mkboards.com/forums/threads/yoshi-too-loves-inward-drifting-bikes.16008/
And, to conclude this, the evergreen Toad combination: