Back up for a second. There are three 'reasons' to back up your data.
1) Disaster Recovery
This protects you from 'a meteor struck your building' scenarios. You need some way of quickly getting your whole servers rebuilt quickly. The classic answer to this question is full system backups. The problem is after some number of days, a large portion of your data is nearly worthless for DR (the OS data, lots of application data that's hugely static, etc).
2) User Error.
This type of backup covers the 'uh, I blew this file away 2 months ago, and it's really important', or 'uh, our DBA dropped this table, but forgot about this monthly report that we need to run one last time' etc. How long you keep these backups is a business decision. I've heard everything from 1 month to 2 years.
This is the REALLY long term backups, often required by government agencies... 'The IRS requires this class of financial records for 7 or 14 years'. The good news is this is usually a small subset of your data. Tapes are good for this, or often optical media.
Armed with these data classes (and a good audit of your environment), you can start classifying what type of data you actually need.
Here's our backup strategy (note: it's a little complicated).
General strategy: Backup to disk, duplicate some data to tape. We run full backups once per month, level 2 backups one per week, and level 3 backups once per day. We keep the full backups for 3 months on disk, and 1 year on tape. We keep the L2 backups for 4 weeks, and the L3 backups for 2 weeks. This gives us high backup 'resolution' for the past 2 weeks, and diminishing resolution, the further back in time you need. On our user shares (netapp), we don't do L3 backups, instead we rely on snapshots. This makes restores a LOT easier to manage.
The big win we have though is that we have 3 'sites'. One of them is the primary site, and our backup environment (disks, media servers, tape robots, etc) live at one of the secondary sites. This is our big protection from the 'datacenter gone' type problems.