eepete is on the money. You want two hard drives. One onsite, one offsite. I replace mine every five years or after the first error of any kind, whichever comes first. Yeah it costs money.... you need to ask yourself how much your pictures/memories are worth. Its kind of like springing for the best auto policy. I find people think having a computer is cheap but it the furthest thing from the truth if you want it done right.
Flash drives and DVD+-Rs are only rated for ~10 years by the manufacturer. But if your data fits in their limited space, I'd go for it. Again, burn two, one offsite, one onsite. Having a backup near your computer during a fire is the equivalent of having no backup. Same with the "media-rated" safes. 10-30 minutes of fire rating is not really a backup plan even when you're next door to the fire company.
I take my offsite drive to my mom's. I backup her stuff and take it back with me. A copy of my stuff is always offsite and so is her's.
Online backups are alright if you have a good Internet connection. I actually wrote the entire frontend/backend for one of them and a common feature is that you can encrypt your entire backup. The one I wrote encrypts each file individually. I think thats better than the archive as a whole (makes restoring one file possible without downloading the whole archive). Its safe because the backup company doesn't [shouldn't?] know your password and the encryption cannot be cracked because its a one way algorithm. The catch with the encryption is that you better not forget the password or the downloaded files are completely useless. Again though, you still need to store one backup onsite. You would be rightfully terrified if you knew how often how little effort went into backing up the online backups at the company itself.
Windows Backup is a fantastic program for home or business use if you're willing to run it by hand or via the Windows Scheduler. I wouldn't download anything else because Microsoft always has all the right "hooks" into Windows to prevent "in-use file errors" and the like.
If your main concern is backing up pictures, you can stick to storing My Pictures/My Documents. But I like getting everything in the backup. You never know when someone put something out of place or when some stupid program stored something you need in it's own directory. I've also had a case where the only copy of a software's serial number was in the registry cause the customer lost the CD and box. Good thing we had a registry backup.
Speaking of which.... don't forget to store all your purchased software's serial numbers in a text file on your computer. In case of fire you're going to be happy you have it. Microsoft Office is one of those programs where Microsoft has no idea what your purchased serial number is even after its registered. So if you lose it, you have no way of proving you own it. None. Believe me, I've been down that road.
I actually tell my prospective clients that I will not do any IT work for them unless they agree to implement all of the above. No way I'm getting a phone call at 9pm some Saturday because they didn't want to spend five hundred bucks. I've even had one guy tell me he doesn't need me then. He didn't realize that was a mutually inclusive statement.
EDIT: I personally run Retrospect 8 Mac and backup all of my servers and laptops nightly to a separate drive. I manually copy the data to the offsite drive approximately once per month and store it a few miles aways. I swap the offsite backup drives to another state every three or four months. So if you're counting, I'm using three backup drives: onsite, offsite local, offsite remote. No, I still don't feel 100% secure but I do feel 99.9%.