I use Flickr. Two thumbs up.
Background: I do my own web design and use open source programs for generating photo albums and such so I've always been very resistant to using free services that I don't have total control over.
I decided to create a Flickr account so I could join some groups and leave comments. Just for shits and giggles I uploaded a few pictures. They have this little "Flickr Uploader" app that you install on your comps. It was so much easier and more reliable than anything I've done, I'm now a paying member. Best Internet service I've ever paid for, period. Any time I upload a pic, it automatically gives me like 5 size choices (including a thumnail or the original) I can hotlink anywhere. Unlimited uploads, plenty of ways to organize and label photos...a lot of stuff I'll never use but it doesn't get in the way. They don't automatically resize and compress your pics like Snapfish did/does. The only thing I'm trying to figure out is if I can do a batch download of all of my files (say my computer crashed and I wanted a local backup of all those photos).