See, while it isn't as amazing as a deck of cards, there are a shocking amount of games you can play with nothing more than to checkers set. Really, an eight-by-eight board with two different colored pieces is some of the most basic components you can get. Checkers is one of the ur-games of history.
A lot of these games aren't new. Some of them have been around for centuries as well, like Fox and Geese, which I understand is good for bar bets, as long as your opponent doesn't know it's been solved. And there are a lot of Checkers variations, some of them regional and some of them just people being wiseacres. (Diagonal checkers, where you turn the board 45 degrees?)
But I'll be honest. I'm not a big Checkers fan. Part of it comes from being taught it too young and not being taught a couple key rules (that you must make a capturing move if you can and that the game can also end if someone cannot make a move)
When I was old enough to understand that there was some real depth to Checkers, I was already into games like Go or modern abstracts like Hive or ZERTZ, dynamic games that made Checkers seem slow and plodding.
Really, the game that really makes me seriously think about using a travel Checkers board is Lines of Action. It's a game about connecting all your pieces and you can only move the exact number of spaces as the number of pieces in that line.
Seriously, it's an excellent game that uses nothing but a Checkers board and feels nothing like Checkers. Truth to tell, if that's all I used a travel set for but I got to play Lines of Actions a lot, I'd be happy.
(Oh, Focus by Sid Sackson. That's another great game you can play with a Checkers set. Also doesn't feel like Checkers, by the way)
Of course, our son is two so I'm really going to end up playing Fox and Geese long before Lines of Action :D