You are confusing 'redundancy' and 'backup'. Raid and off-site is not one against another, they can (and better) exist at the same time.
First of all, a raid 'backup' is continuous, you don't loose anything if you have a HD failure. But off-site backup? Yes, you can purchase those online service, which can be set up every 5 minutes, but the cost? And do you trust your personal photos, all data to a small company? And is your internet bandwidth good enough? I don't know about others, but most plans Comcast offers has only 5/10 Mbps upload. And you wanna backup your 500g photo library and 300g music library? The backup is going to take forever.
And yes, you can just use a portable hard drive, copy everything off your computer and put it in your office or in your car. But how often will you update your backup? Once your computer/HD crashes, and you realized you haven't updated your backup for half a year or longer, then what can you do?
So I believe RAID is actually the best insurance policy if I have to choose in between. Really, the only thing you have to worry is like fire. A theft? I mean if I were a theft, even I like tech gears a lot, I'd rather go looking for other stuff like cash, rings, watches. A hard drive is worth nothing, you can buy a new one with like $100, I won't steal that. And the raid system is a 'set-and-forget' system, really, usual people don't have that much time and effort to manage their backup solutions, and they'll probably forget the system once set up until they need it.
If you want some extra safety, then off-site comes into place, just grab a portable HD with your most valuable, must have data, and put it somewhere else.
Just think, off-site is against fire, and raid is against HD/computer crash.
What's the odds of fire vs HD crash. Fire is wheather, and HD crash is when.