Guild Wars is coming out soon. I know it's an MMORPG but it's got no monthly fee, is made by former Blizzard/Battle.net employees, and is supposed to be based more around strategy instead of number of hours invested into tracking down rare items and such. The design motto was, "spend most of your time having fun, not preparing to have fun."
Civilization III is a good choice, as it's a strategy game that revolves more around actual strategy and less around memorizing hotkeys and building up heroes (*cough* Warcraft III *cough*).
My entire family, parents included, enjoyed playing the Mario Party series of games on N64. They've got some out now for GameCube but we haven't tried those. Not sure if you've got either one of those consoles.
Also, there's two old-school computer games that you both might enjoy (at least, I certainly like them, and they don't involve reflexes or mouse skill). First is NetHack, a hack-and-slash RPG that started as Hack, a game for the BSD flavor of UNIX. It's the world's oldest computer game still in development, and you can get it from
www.nethack.org. It's an extremely deep game with a learning curve that has grown steeper with each new release.
Yet Another Nethack Site can help you overcome it. Once you learn your way around (which took me about 2 weeks), you'll find it to be very addicting. Plus you can find a version of it for just about every platform. I don't think the dev team will be satisfied until you can slay kobolds and loot treasure chests on your alarm clock.
The other is Hexxagon, a game released when I was just a wee lad. I remember playing the original shareware version of it on my dad's IBM. It was one of the first 3 1/4" floppy disks I had. It's free shareware, and I don't think the company that made it even exists anymore. It still runs on WinXP. If you'd like a copy of it, PM me and I'll email it to you or something-- it's small.
There's a Java applet version of it
here, but it just isn't the same to me. The sounds and the computer opponent are just not as good on the Java version.