Decidability Problem
Let P(M,q,w) = "the computation of M on w visit q"

If we suppose P décidable, then the problem P' defined as :

P'(M,w) = w \in L(M) 

is decidable.

Proof : 
This a decision procedure for P'. Let M be a machine and w a word. 
For each accepting state q of M, we run P(M,q,w).  If the answer 
 is "yes" for some q, we return "yes". Otherwise, we return "no".

Since it is well known that P' isn't decidable (Rice theorem), we conclude P isn't decidable.