~snip~
The best approach is to:
1. never have online backups.
2. always have two backups on physical media, in two different locations.
Just do that and you 'll be better than 90% of users who still keep money on exchanges.

I'm not really convinced about the never having online backups. If you encrypt them with a strong enough password, then it should be pretty safe.
If you think about it, every Bitcoin address has a unique "password" and is "stored online". If you have a strong password for your keys then it would be as safe as anyone trying to guess your key anyway.
Of course, unencrypted keys, or keys encrypted with a weak password would be easily compromised if found online.
Yes, about the multiple backups, that's really a good idea. At least 2 independent backups, more if possible.