Transfer ITunes Library to New Computer

The policy on music/media purchases is that you only get one download and it's up to you to maintain a backup against loss: iTunes Store: Purchased content can be downloaded only once

The licensing of Purchased applications allows for them be downloaded over again, see this article for details: How to redownload purchased applications from the App Store

If you have an iPod that still has any of your purchases on it you'll find details in this article on how to transfer them to the computer: Copying iTunes Store purchases from your iPod or iPhone to a computer

Failing this, you could try contacting iTunes Store Customer Service and you might be able to persuade them to sanction a second free download. There have been occasional reports in the iTunes forum of this happening, however just be aware that they are not under any obligation to do so. If you click on this link it'll take you to the support/contact page, from there click on Music Purchases then the Lost or Missing Items option, from there click on "Email Us": Customer Service - iTunes Store Support

You might also want to check out these pages for future reference:
How to back up your media in iTunes
Back up your iTunes library by copying to an external hard drive