The most common is muay thai, supplemented by boxing training.
MT for learning how to use the 8 points effectively, boxing to improve footwork/ defense/ head movement/ hand proficiency. At the highest levels in MMA, it seems that everything starts with the hands. Fedor, BJ, GSP, Anderson, Aldo- all the guys that have been talked about as potential #1 p4p fighters, they all have excellent proficiency with their hands. Sure, Aldo & Ando both blast guys with kicks & knees without setting them up with hands at times, but they both have great boxing.
From experience, I can tell you that since you are focusing so much on learning proper offensive technique for the multitude of different strikes, defense can be overlooked in Muay Thai classes. In a boxing class, footwork & defense are equally (if not more) important to solid offensive technique with your hands.
Edit: That's if you're just starting your training, and not to say that guys with Karate/ Sanshou backgrounds can't come in and do well. But even then, MT and western boxing are necessary to train in since they are so prolific in modern MMA.