Functions which, when called with the right (or the wrong) initial set of parameters, call themselves, causing themselves to call themselves again, and so on ad infinitum. The simplest example would be, in C++:

void foo()
{
    foo();  //Calls foo, which calls foo, which calls foo...
}

Given finite computational speeds and call stack sizes, functions which try to recurse forever are generally considered (at least in computer science circles) to be a Bad Thing.

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Dekaritae: Well, it's infinitely recursive in theory...

Speaking from a purely technical viewpoint, don't the statements of the limitations of computing power and finite time of existence mean that the function is not an infinitely recursive function, but merely a recursive one? Seeing as the function could not practically go on forever.