I actually spent the first year or so of building computers without using a wrist strap. I was also always careful to ground myself every few seconds, usually against the metal of the case. I've only had one part fail from those days, and that was one where the computer shop (which pre-jumpered the mobo for the CPU as a "free service") jumpered the mobo for the wrong core voltage.
Still, it's a good thing to have. One of the ten-dollar ones, cloth with interwoven metal threads, does just fine. Or you could make your own.
It's also a good idea to be careful what you lay your components on. There's a whole host of material that's classified as hazardous to static-sensitive componets: paper, some plastics, styrofoam (BIG bad), most bubble-wrap, cardboard, wool (of course), some adhesive labels, and pretty much any synthetic textile fabrics (nylon, spandex, etc). Cold, dry days (like the dead of winter) are days when static electricity is at its worst. Friction (rubbing your feet on wool carpet) and separation (peeling a sticker off its backing) are invariably what cause static.
Now just to make you paranoid, you may not even feel the static shock that kills your components.
As for materials that are guaranteed to be static-safe: silver/plastic anti-static bags, the anti-static pads you might get at your local computer store, and (usually) whatever your components come packed in. A lot of stuff that's static-safe is color-coded pink, but obviously, not everything that's pink is safe!
Kelledin
<font color=red>"Step away from the gimp suit and put your hands on top of your head."</font color=red>