Most answers deal with the overhead of virtual functions, but there are other reasons not to make any function in a class virtual, as the fact that it will change the class from standard-layout to, well, non-standard-layout, and that can be a problem if you need to serialize binary data. That is solved differently in C#, for example, by having struct
s being a different family of types than class
es.
From the design point of view, every public function establishes a contract between your type and the users of the type, and every virtual function (public or not) establishes a different contract with the classes that extend your type. The greater the number of such contracts that you sign the less room for changes that you have. As a matter of fact, there are quite a few people, including some well known writers, that defend that the public interface should never contain virtual functions, as your compromise to your clients might be different from the compromises you require from your extensions. That is, the public interfaces shows what you do for your clients, while the virtual interface shows how others might help you in doing it.
Another effect of virtual functions is that they always get dispatched to the final overrider (unless you explicitly qualify the call), and that means that any function that is needed to maintain your invariants (think the state of the private variables) should not be virtual: if a class extends it, it will have to either make an explicit qualified call back to the parent or else would break the invariants at your level.
This is similar to the example of the infinite loop/stack overflow that @Jon Skeet mentioned, just in a different way: you have to document in each function whether it accesses any private attributes so that extensions will ensure that the function is called at the right time. And that in turn means that you are breaking encapsulation and you have a leaking abstraction: Your internal details are now part of the interface (documentation + requirements on your extensions), and you cannot modify them as you wish.
Then there is performance... there will be an impact in performance, but in most cases that is overrated, and it could be argued that only in the few cases where performance is critical, you would fall back and declare the functions non-virtual. Then again, that might not be simple on a built product, since the two interfaces (public + extensions) are already bound.