First what not to do:
Don't invest in RAID-5 or RAID-6 arrays unless you can afford a high quality controller and SAS drives. Cheaper RAID arrays often have significant problems rebuilding. They're also expensive and large. You're also gambling that you choose a hard drive model that doesn't have any serious systemic problems. Choose poorly and you're risking total data loss. Besides, they key desired feature here is mirroring and one doesn't need RAID just for mirroring.
Forget about recordable DVDs or BluRay discs. The media capacity is small and thus cumbersome to mange. The recording dyes can degrade surprisingly fast, again varying greatly with manufacturer or lot. There's lots of research on this and you can download software to measure correctable errors before the discs become unreadable. I've had some discs become unreadable within 6 months. Some discs test with significant error rates immediately after being burned, before even leaving the drive tray. Basically if you're not testing error rates of your dye-based media, the joke's on you for buying them.
Tape drives are inconvenient for random access. Longevity could be better or worse than hard drives. Without hard data one can't recommend tape drives. Like everything else, longevity probably varies quite a bit between media brands and drives/recorders.
Internet backup services aren't going to scale depending on how much you need to access.
Here is what I do to manage about 3 TB of family photos and video, including about 0.5 TB of encrypted (truecrypt) content. Its not a perfect solution. However its cheap and easy to set up and maintain.
1) I have several "master" directory trees on my main computer. It runs Linux currently, but windows could work too. There are several drives and partitions, all mounted in a master "media" directory tree. There are subdirectories organized by year for which the media was generated. This helps with locating media of interest.
2) I have a large number of 1 to 2 TB external USB 2.0 hard drives from different manufactures (mostly Seagate and WD branded external drives from Sam's or Costco), each one clearly labeled. Some have one partition. Some have two partitions with the second partition being a truecrypt partition. The external drives are grouped together such that each group is a complete backup.
3) For each drive I have a unique shell script that calls the 'rsync' command.
4) I keep one group of drives at my house (the local backup), a second group in a bank safety deposit box and a third group at a family member's house. So that's the original plus three backups.
5) I sync the local backup about once or twice per week, or after significant media generation. This only takes a few minutes and is fully automated.
6) Once every month or two I will do a local sync, swap the local with one of the other groups then do another sync.
7) I periodically reformat the drives and check the SMART data.