Nowadays most common radio receivers are with 6 and 8 channels but you can find versatile 2.4Gh radio systems with up to 16 channels.
According to the adopted modulation, radio receivers can be categorized in:
Just few of the best radio receiver brands: FrSky, Futaba/Spektrum, iRangeX, RadioLink, FlySky and Walkera.
Tough question, When it comes to choosing one I would personally suggest FrSky radio system for multi-rotors but I also like the much cheaper FlySky radio.