Stockfish

Commercial chess engines (Rybka, Fritz, Chessmaster) are amazingly strong, but they cost serious money. But there are also very strong engines that are freeware. Mig Greengard discusses several in this blog post, including Stockfish, which you can download here.

Please note that if you don't have a commercial interface (Fritz, Shredder, Aquarium), you'll need to download a UCI interface.  I'm told that Arena (download here) is a good free interface for Windows users.  More information (but not much more!) is available on the Stockfish FAQ page.

So how strong is Stockfish? Engines are funny things: the ancient version of Fritz (6.0) on my office PC solves the following position  almost immediately, Rybka takes a second or two, but Stockfish takes a while to find the solution.  That doesn't necessarily mean that Stockfish is weaker, however.  When there's a forced variation with several "studylike" moves and a main line more than ten moves deep, the stronger engine will sometimes take more time to find the correct solution: aggressive alpha-beta pruning eliminates "silly" moves from the computer's search.  Sometimes silly moves are brilliant, but more often they're not. 

We humans are much better at making these judgment calls; our silicon friends are millions of times faster than us, however.

A test position (my favorite study!)

FEN: 2b4k/8/5Pr1/5N2/8/8/8/K1B5 w - - 0 1

Korol'kov 1951
White to play and win

This beautiful study is worth thirty minutes of your time.  Understanding why certain moves don't work is (as usual in a study) a big part of the fun.  You can then cut and paste the Forsythe notation into your chess engine to get its answer.  Please let me know your performance results!

There's a YouTube video explaining this study.