I happen to have a good example which is part of my life that shows how this is a problem.
I come earlier than the normal worker to the office, so it's pretty calm and nobody's around. Also, I always leave my computer on, and it usually keeps on on its battery from one day to another (it's a notebook and I leave it sleeping). However, when I come in on Mondays, the battery didn't hold so a long startup session commences, and then the corporate virus scan runs, all my dev services starts up. I might as well have half an hour where I can literary do nothing on the computer.
First approach is try to avoid it.
If possible, avoid those times happening. On my case, I could find out how to make the computer hibernate, or how to prevent it from taking so long on its startup. If you're dealing with downloads, then maybe do something else and leave stuff downloading when you're out to lunch.
Second approach is to be prepared.
As others correctly said, it would be a good idea to make use of that time. I am thinking in bringing in a book, or even better, my iPad, so I can read a book or start checking emails right away while my working machine starts up. You may want to do pushups as Casebash said, or check email, or get some coffee. Whatever would interrupt you later and you can do in this little time, is a perfect candidate for doing on those dead times.
Third approach (complementary) is to start identifying them.
I think that if you're asking this question, you're on the right path, but there are possible some other dead times and interruptions that are not as obvious as my example and you still deal with them day to day. Start thinking about those (you can even use those dead times for it!) and how you could avoid them or use that time in a better way.
Also, really good question. So good that you made me write advice for myself.