I use a tripod for the majority of my shots. Even after trying all the handhold tricks (hold your breath and release slowly, keep camera close to your body etc.), I am just ever so slightly shaky. That tiny bit of camera shake really makes a difference. The things I like to shoot - macros, some landscapes, still life - make tripods virtually a must. Lately being in the
threesixtyfive and
fiftytwo flickr groups and shooting the self-portraits they require, I find my tripod invaluable.
I know tripods can be hard to carry around, so I also have a monopod. Generally I use handheld only when doing candids or when a tri- or monopod is impractical.