At any time, a proper setup involves maintaining a minimum of three copies of any important data:
1) The copy you use.
2) Your local backup.
3) Your off-site backup.
How you choose to implement those can vary. For instance, if you have the cash, I think most of us would agree that maintaining separate RAID arrays for your in-use and local backups would be ideal. The reason you'd keep them separate is because of the all-important mantra: RAID is not the same as having a backup (you don't seem to be under this misconception, but it bears repeating, nonetheless). RAID can protect against certain forms of hard drive failure, meaning that you wouldn't even need to resort to using your backups in the case of those sorts of failure, but it does nothing to protect against your data being corrupted by the file system or deleted by an accidental action on your part.
If you don't have the money for RAID, you could start out by just putting your in-use and local backup copies on separate hard drives (which it sounds like you're already doing), the first of which backs up to the second. That'll work most of the time and in most cases, but it means that hard drive failures will be more of a threat and an inconvenience, since you'll have to be more reliant on your other copies being intact, given that you'll be suspending your use of the damaged copy while you replace the drive and restore the data to it.
In addition to your local copies, you should have an off-site backup in a location that is geographically removed from you, that way if natural disaster does its worst, you don't lose your data. CrashPlan is the one I use and is a good place to start, since it offers multiple options for backing up off-site, including a free option where you and a friend provide off-site backups for each other. Their for-pay options are reasonable in price (though they have more than doubled since I joined a few years back), offer unlimited storage, and provide the ability to set your own encryption key (i.e. keeps them from being able to pry into your data if they're served with a warrant).
So, at a minimum: a drive for your in-use copy, a drive for a local backup, and CrashPlan backups to a friend, all of which would only cost you as much as the hard drives involved.
Ideally, however, you'd also do something to protect against corrupted data or accidental deletions on your part, which means storing multiple versions of your backups, and doing so both locally and off-site. CrashPlan subscriptions all provide full versioning of anything you backup in perpetuity, so if your data becomes backed up in an incorrect state, you can rollback to a previous version easily. Even so, you should still have versioning stored locally in some form or fashion, that way you're not dependent on CrashPlan always being around and always working. If you're a Mac user, Time Machine can serve this purpose (it should be in addition to any other local backups mentioned above), and you can even backup your Time Machine data off-site if the off-site backup system you choose doesn't offer built-in versioning like CrashPlan does. I'm sure others can make some recommendations for Windows and Linux alternatives to Time Machine.
And yes, you should keep the tapes around, if only so that you can demonstrate ownership should any legal questions come up. But once you verify that the copies you've made are all correct and working, you can probably box them up and put them in an out-of-the-way spot in the attic where you'll never have to bother with them again.