I think this is highly industry-specific. In the restaurant business, there's a saying: If you've got time to lean, you've got time to clean. Essentially everybody, whether front or back of house, is expected to clean in their downtime. But I think if you saw a lawyer or accountant tidying the mailroom and doing the recycling, you'd think "haven't you got someting better to do?" A tech support role is between the two. I'd expect you to clean up your own messes, and perhaps to do a quick 5 minute cleanup in the kitchen or mailroom while standing around waiting for coffee to brew or a photocopying job to finish, in other words when you're in that room anyway.
For longer gaps, the ideal task
- looks exactly like working - you sit at your desk, you have your headset on, you have your hands on the keyboard
- is entirely interruptible when a real call comes in
- improves your performance
There are lots of ways to improve your performance. You could get better at your job. For example you could be watching an online course related to the technologies you support. You could relax and improve your mood by reading funny or interesting web sites. You could be active on this site and ones like it, or on Twitter.
You could also take care of virtual tidying by running backups or checking reports or looking through the new items in your worklist, or taking some notes for your year-end review. If you know the time gap will be significant, you could be writing scripts for things you do a lot, or setting up a new system you plan to experiment on but be careful with those kinds of tasks - they can be hard to stop when you're supposed to switch back to your main job.
A bad task
- tells everyone from 50 feet away "I have no real work to do!" Cleaning up a mess you didn't make does this
- is embarrassing if someone else sees the details. Personal Facebook does this
- lowers your performance - by upsetting or distracting you, encouraging you to dislike your work, etc
Most non-technical web sites are going to be bad tasks. Don't get in that habit even if your peers do.
If you have a headset, and it has a good range, you can also go for a walk around the office. This is slightly less boring than staring at your screen and good for your energy levels, but you aren't going to miss a call if one comes in.