Yes, for example TMSAT (Turing Machine SAT):
TMSAT = $\{ \langle \alpha, x, 1^n, 1^t \rangle : \exists u \in \{0,1\}^n$ such that $M_\alpha$ outputs 1 on input $\langle x,u \rangle$ within $t$ steps.$\}$
(Theorem 2.9 of Arora-Barak. See Chapter 2 draft: http://www.cs.princeton.edu/theory/index.php/Compbook/Draft#np)
It is quite easy to show that this problem is NP-complete!