Wrist bands don't REALLY work. The cheap ones don't ground better than the circuitry does (oops), and the good ones have resistors built in so it doesn't ground too much through YOU, and melting your socks to the carpet (well, melting the wrist band to your arm). Personally, I've always lived by the same rule these others do, and maintain contact with the case, at least when I remember to. I leave the computer plugged in, to ground the case, or else it may ground through the motherboard to the floor, or something - at least that's my theory ;-),. But my brother seriously zapped my mother's computer the other day (and he's worked in electronics manufactoring for 10 years) - it arced from the board to ground - grounded something that wasn't supposed to be.
But you ground the wrist strap by plugging it into the ground hole of a power socket.
And, you aren't risking a thousand dollars of equipement, unless the stactic arcs from you to the CPU, and which happens to arc to the HDD, which happens to arc to the video, which it turn takes out your sound card, etc.... You see the point - it's be worth a grand to see the laws of physics suspend for an instant, assuming you live through it. One, maybe two components would be fried in the WORST possible scenario.