You can usually find traditional instruments of rock like guitars, bass guitars, and drums. Vocals can be sung, rapped or both. You may also see electronic sampling equipment, scratch pads and a DJ.
Now here's the part that some kiddies can't seem to get right: Rap rock is a broad definition for the hybrid genre. Nu metal and rapcore are just specific examples of rap rock.
Nu metal tends to be heavier, harder music with electronic elements, it leans more towards metal (hence the name). Bands such as Slipknot, KoRn, and Godsmack fall into this category.
Rapcore is more of a hybrid between rap and hardcore punk (instead of metal). Bands like House of Pain, Limp Bizkit, Linkin Park, Rage Against the Machine and some of the works of KoRn are good examples of this genre.