Randell,
I've been shooting with an SLR since 1980 and have never owned more tripod than a little pocket-sized one (and that seldom used). I've shot slides in European cathedrals in ambient light, landscapes, and many people accepting diplomas, all handheld or propped on the nearest stationary object. Church pews, rocks, architectural elements all make excellent stabilizers. Frankly, a cable release will go an awfully long way to reducing motion for most practical purposes, and a cable release weighs a hell of a lot less than any tripod. The only time I have ever used a full-sized tripod was when I was documenting an exhibit installed in the architecture library at Battle Hall at UT. I've just never felt like lugging one around. I'm sure there are shots I've missed, but I couldn't tell you what they are. I've taken more than my fair share, and don't recall any disappointments ever being for lack of a tripod. FWIW....
TG