I don't wear a wristwatch: it's too uncomfortable, and I don't need to know the time often enough to make it worthwhile. However, the watch form factor can be used for other purposes; wristwatch calculators, organisers and radios have all been around since the 1980s.
I'd like a watch that I could program myself -- essentially it'd be a low-powered computer with a few hundred kilobytes of RAM, some buttons and a high-resolution display. Add some Flash storage and a USB interface with a folding plug (which exists already in wristwatch form), and you could have a music player, portable data storage device or notes browser.
To improve ergonomics, we could make it a pocket watch instead (which has been suggested by other people). For more display area, or more usable-sized buttons, have a folding pocketwatch; there's no need for it to be round. Alternately, I nearly always carry my keys with me, and have various other tools attached to them: I could replace the plastic keyfob with a version that includes a little builtin computer.
Developing software for a watch would be an interesting challenge: it needs to be able to run for very long periods of time with only the energy available in a small battery (or, with some smart design, with kinetic energy as some mechanical watches do: it'd be really neat to have a computerised watch powered by a spring!). The PalmOS API was designed for palmtop devices, and worked very well; something cut down even further -- with explicit support for power control, and moving between a micropower "just the time" state and a more expensive mode where the rest of the CPU is powered up -- would be necessary for a watch.