What are some great ways to take advantage of bitwise operators?

Constant time 2-exponentiation:

x = 1 << n; // x = pow(2, n)

While I agree with Michael McGowan in general, bit twiddling hacks can be very useful in certain situations, for instance when programming embedded hardware which doesn't have all the usual instructions. I've also had good use for such techniques when encoding programs into theorem provers such as SMT solvers, which didn't support all the operations I wanted to use.

My first stop when looking for a bitwise solution to a problem is the site bit twiddling hacks. It has quite a few code snippets for many of the most common techniques.

Then there's also the book Hacker's Delight covers a few bitwise techniques in depth.