The better question might be "Why does C# have non-virtual methods?" Or at the very least, why aren't they virtual by default with the option to flag them as non-virtual?
In C++, there is the idea (as Brian so nicely pointed out) that if you don't want it, you don't pay for it. The problem is that if you do want it, this usually means you end up paying through the nose for it. In most Java implementations, they are designed explicitly for lots of virtual calls; the vtable implementations tend to be fast, scarcely more expensive than non-virtual calls, meaning the primary advantage of non-virtual functions is lost. Furthermore, JIT compilers can inline virtual functions at runtime. As such, for efficiency reasons, there is very little reason actually to use non-virtual functions.
Thus, it largely comes down to the principle of least surprise. It tells us that all methods to behave the same way, not half of them being virtual and half of them being non-virtual. Since we need to have at least some virtual methods to achieve this polymorphism thing, it makes sense to have them all be virtual. Furthermore, having two methods with the same signature is just asking to shoot yourself in the foot.
Polymorphism also dictates that the object itself should have control over what it does. It's behavior should not be determinate on whether the client thinks it's a FooParent or a FooChild.
EDIT: So I'm being called on my assertions. This next paragraph is conjecture on my part, not a statement of fact.
An interesting side effect of all this is that Java programmers tend to use interfaces very heavily. Since the virtual method optimizations make the cost of interfaces essentially non-existent, they allow you to use a List (for example) instead of an ArrayList, and switch it out for a LinkedList at some later date with a simple one-line change and no additional penalty.
EDIT: I'll also pony up a couple sources. While not the original sources, they do come from Sun explaining some of the workings on HotSpot.
Inlining
VTable