What is the best way to backup photos & videos from iPhoto online?
First option, there are some excellent services that provide online backup solutions for a reasonable price. Two examples are Mozy and Backblaze. The advantage is that you can set it and forget it, and it will back up all your files (with options for some things you might want to exclude).

Another option is using Dropbox. You can move your iPhoto Library from your Pictures folder to the Dropbox folder and alias it to the original location (drag using ⌘option to make an alias instead of a copy). If you don't alias it, iPhoto should just ask you where the library is stored when you relaunch it anyway.

I don't really think of services like Flickr as backup, they're more of an online photo organizer, but yes they can be used that way too. There is no synchronization, so you have to upload your updated files manually.