How long have you had the drive?
How is it formatted?
How is it connected to your iMac?
If there's no files on the drive that you don't have on your iMac try erasing it, formatting it OS X Extended (journaled) and start over from scratch with Time Machine. See if it will complete backups. Remember the first backup will take a while as it's a full and not an incremental backup.
If you decide to get another drive for Time Machine I recommend drives from OWC (MacSales.com) as they have proven reliability, excellent customer support and warranties. Consider this model in a size that's about 2-3 times the size of what you're backup up.:
OWC Mercury Elite Pro -HDD
