I'll throw in another vote for backing them up on dvd if both the computers can read dvds.)
Otherwise I'd back them up on cds.
I have about 120 gb of music files backed up on over 100 cds (started before dvds were a viable option).
I used to run 1 pc with multiple hard drives, with the same files backed up on multiple hard drives, figuring that would be foolproof.
Well, I had multiple hard drives fail over a period of 3 days, and if I didn't have the files also backed up on cds, I would have lost most of the files.
I also had a few friends with external hard drives for all their backups that had the external drives fail, & they had to say goodbye to all their backed up data.
With the price of blank dvds nowadays, I shifted from blank cds to blank dvds to do backups. Saves a good amount of storage space & is more economical as well. When I start to run low, I buy a few 100 disk spindles of dvd+r discs when they are on sale at best buy (last week I bought 2 spindles of fujifilm dvd+r for $24.99 each there). That way if I run out in between sales, I don't have to pay the regular price for them.
I've had great luck with TDK, Fujifilm, Sony, and Philips discs. The only coaster I ever burned was when the power went out in the middle of a burn.