For sheer brain-stretching there's nothing quite like group theory and number theory, which have relatively few prerequisites and the latter of which comes up surprisingly often in programming (anything where you're using %/mod).

The theory of generating functions (known in the math world as Formal Power Series) is just insanely useful.

Galois theory (field extensions, finite fields) comes up in coding theory and cryptography.

If you learn about p-adic numbers and p-adic analysis then you'll understand why 2s-complement arithmetic works (and then kvetch about the lack of a proper 2-adic division instruction in hardware :-)

If you're doing graphics programming then linear algebra and trigonometry matter matter a lot. Spherical trigonometry matters if you're doing anything with cartography, or GPS/navigation. Hyperbolic trigonometry would be more brain-stretching. Projective geometry (if you want to understand why those 2x3 matrices come up all over the place when talking about scaling/rotating/translating)

Calculus, on the other hand, comes up surprisingly non-often unless you're doing work in physics or statistics. (I always thought the high school math curriculum should go straight into group theory and number theory from plane geometry rather than the comparative dead-end of calculus, but hell will probably freeze over first)