Flickr's definitely a very powerful and popular service now. The Flickr Pro accounts are $25 a year and offer unlimited storage (See:
Flickr: Upgrade to a pro account) and may be the type of photo service you are looking for.
As for online storage, here's a review of them (albeit a few years old):
The Online Storage Gang
Both Xdrive and Mozy have been around for quite some time, most offer some kind of trial option you can play around with to see if their service is the right one for you. I personally prefer backing up my files to a USB hard drive, in addition to backing up to DVD-R and storing that in a different offsite location, such as the Western Digital My Books:
My Book Overview