You may only download songs from iTunes once. They have documentation on their site about how to backup your songs to CD.
That said, you can contact Apple to have your songs made available for download again, at which point they will flag the songs as reimbursed or otherwise non-downloadable again for your account. There’s a way to do this through your account iTunes, it’s pretty straightforward.
I had to do this a few months ago, and made at least three copies of all the music I had downloaded. Fortunately I only had about a DVD worth of music to backup :-).
You are allowed to access the songs with up to 5 computers, and I don’t know how many iPod/iPhones. You can deauthorize all computers that previously were authorized and readd them through iTunes when you try to play songs you purchased.
Yes, this is now possible, Apple introduced this feature to iTunes in the Summer of 2011.
Apple now allows downloads of Past Purchases including music, thanks to the new iTunes in the Cloud feature.
Using iTunes 10.5 and/or iOS 4.3.3 or later, you can log into your iTunes Store account and go to the Music Store and click on (Past) Purchases. On the iPhone it’s under the iTunes app in the new “Purchased” tab.
I had to deal with this recently.
When I had finished re-installing (this was on OSX) I connected my iPod to iTunes.
I then right-clicked it and selected an option called something like “Transfer Purchases”.
This transferred my purchased files from the iPod back to iTunes.