Is there any task where classical computers outperform quantum computers? Everybody knows that there are whole classes of problems which quantum computers are able to solve much faster (i.e. with fewer instructions) than classical computers.

Is there any problem for which the reverse is true?
If you're asking whether a quantum computer can compute any function that a classical computer can compute without using many more elementary computational steps, then the answer is yes: a quantum computer can perform any reversible classical computation, and if you keep the input around, any classical computation can be made reversible at a cost of multiplying the number of steps by a small constant factor.

If you're asking whether a quantum computer can compute any function that a classical computer can without using many more resources, the answer is much less clear. The construction that lets you make a $T$-step computation reversible using $O(T)$ steps also takes $O(T)$ space (i.e., memory cells). You can achieve a smaller blow-up in space at the cost of a superlinear number of steps. See Time/Space Trade-Offs for Reversible Computation by Charles H. Bennett. 

For an actual physical quantum computer, it's very likely that you might also be able to make it faithfully simulate a classical computer by letting it lose coherence, but in this case it's no longer really working as a quantum computer, and if you try to use a quantum computer that is operating this way as a subroutine in a quantum computation, it might not work properly.