While looking around the web for inspiration, I found a game called simply "Font Game" on the popular type blog I Love Typography. It was a standard multiple choice quiz where you have to identify a typeface by name from four options. Give it a try here. I was very bad at it. Anyway, after playing Font Game I decided to see if there were any other typography-themed games out there. Here's what I found:
Kern Type is a game from design website Method of Action in which you adjust the spacing between the letters of a given word and then compare your solution to that of a professional typographer. The closer your solution is, the more points you get. It's a fun way to hone your kerning skills.
Shape Type is made by the same people who made Kern Type. It's similar in concept, but instead of kerning you adjust the shape of an individual letter using handles (similar to those in Illustrator) to make it as balanced and aesthetically pleasing as you can.
The Anatomy of Typography is a timed quiz where you need to click on different parts of the letter (for example, counter, crossbar, etc) to identify them. Very simple, but very helpful if you're trying to memorize.
TypeConnection is a "typographic dating game" that allows you to match up typefaces that work well together. After picking an initial typeface, you choose a strategy to use in combining it with another. Then you are given several fonts to choose from, and you can read about their histories and compare their characteristics before picking which one to use. If you make a successful match, the game will tell you about why the typefaces work well together. Not only is this game interesting and educational, it is also kind of adorable.
I Shot the Serif is more of a just-for-fun game than a resource for practice, but this list would not be complete without a good old-fashioned shoot-'em-up. The premise is simple: click the serifs, and avoid the sans-serifs without running out of time.