"What do you believe?"
Nah. It should be correct, though in modern speech, they only use the pronoun only once when making a new topic. So if you were giving someone an interview and you ask him what he believes, all you'd need to say is "Cosa credi?" But if you're a Christian missionary and you walk by someone's doorstep to ask them what they believe in, you'd say "Cosa credi tu?" since you haven't met them.
Italian verbs often don't need the subject because it is already included in the ending of them. (You eat = tu mangi = mangi) ( what do you eat = cosa mangi?) (what does she eat = cosa mangia?)
just had to comment that i love that one of the translations of 'che' is trans-Amazonian.
Would "Cosa pensi?" be wrong? Does the verb pensare ever mean believe instead of think?