Classical algorithms can solve 3-SAT in $1.3071^n$ time (randomized) or $1.3303^n$ time (deterministic). (Reference: Best Upper Bounds on SAT )
For comparison, using Grover's algorithm on a quantum computer would look for and provide a solution in $1.414^n$, randomized. (This may still require some knowledge of how many solutions there may or may not be, I'm not sure how necessary those bounds still are.) This is clearly significantly worse. Are there are any quantum algorithms that do better than the best classical algorithms (or at least -- almost as good?)
Of course the classical algorithms could be used on a quantum computer assuming sufficient working space; I'm wondering about inherently quantum algorithms.