If you ride a lot in traffic it's good to have a bell. And reflective bands and a small blinky front and back even if it isn't nighttime or winter. It can be surprisingly dark on a grey, rainy day. Winter/nighttime - BRIGHT lights.

I just mounted a mirror, a bit early to tell but it saves me from having to turn around all the time. It's not quite stable though and tends to shift when I ride over bumps. I've also seen many riders with mirrors that don't look in them, though, I've come up behind them and their mirrors are askew and useless, or they never glance down at them.

A computer is fun but not necessary unless you're training. Lock - a light one can be handy if you need to pop into a store or something. I don't usually carry a pump or any mechy stuff on my commuter/mtb, I ride places where I can bus or walk home and I rarely flat on mtb tires. On my road bike I always carry a seat bag with 2 tubes and 2 co2 cartridges, plus some spare cash.