Once you know some basic combos, they'll flow together. I'm from a boxing/brawling background, so my hands fly.
The regular left jab-right cross-left hook is always there (assuming orthodox stance), whether the hook goes to the liver or head. What I've seen is that if the liver is hit cleanly, or in that general area, I could come back with a right upper then a right cross and another left hook. The opponent's body just seems to bend into these moves for me...so don't get mad if it doesn't work for ya hahaha
Then there's some leg work combos. A lead kick to a right cross or hook feels natural for me, then a left hook to the body and finishing with a right kick to either leg, body or head.
One of my favorites, I haven't been able to pull this off because in the tourney i'm training for...I can't use knees.

There's the standard left jab-right cross-left hook followed by the rear knee. Alistair Overeem did something like this in his last K-1 tournament, where following the rear knee he'd throw a same-side hook. Maybe the momentum of the rotation's already there.
Oh! And Gohkan Saki's combinations. Where do I start?? Just watch some stuff, and you'll see some nice "combo breakers".
