Backup is a near religious issue. Everyone has their own beliefs, and there is precious little in the universe that will shake those beliefs when they've been learned "the hard way". With that said, I'll give you my opinions on backups.
Backups are your last resort. You use them only when everything else has failed. In spite of that, they are your last resort and when you need them, you really, really need them.
You want to get the most recent backup (like last night's) off site as quickly as possible. If the backup media (tapes) are in the same building as the machines they have backed up, the disaster that destroys the machines will also destroy the backups! Depending on how critical the backups are to your business, it is usually worthwhile to take them offsite as soon as they are complete.
There isn't much point in keeping old backups off site. If you have the space to store them onsite, there isn't any reason not to store them there, and there are lots of practical reasons why you should. Many files change very little if at all from day to day. Being able to easily grab a two day old file can be very convenient.
Backup media isn't really important anymore. Tape works well, DVD autochangers are very good, and if you can afford it either removable disk or telecommunications to a hotsite are even better. Don't get too worked up about the backup media, as long as you are certain that it is reliable.
Backup is cheap these days. Compared to not having backup when you really need it, backup has always been cheap. Backup is not a place to cut corners, I've never heard of anybody being fired for having too many or too good a backup!
-PatP