I have both Flickr and Photobucket. Flickr only because Yahoo Photos will no longer be in existance come next month, and all my pictures would have been lost in cyberspace for ever. And Flickr is a Yahoo partner and was easily accessable. But I personally don't like it as much as I did Yahoo photos. I agree with what many have mentioned before, Flickr takes a while to come up, and although it has many different ways to organize your photos, in doing so it just makes the page take even longer to come up, and more buttons to click to actually get where you want. It also has a free account
and a paid account, and in hoping you get a paid account, they limit the number of pictures you can upload in a certain time, and there are many annoying ads. The only reason I have it is because it saved my 100s of Yahoo pictures before they were lost forever, and I can also display them on my Yahoo 360 blog because, well, it's fun to see pictures in a blog!
I opened up a Photobucket account a few months ago because I tried linking to a picture from Flickr in a blog and it didn't work so well. But I heard how easy and carefree Photobucket is. And what I heard was right. They lay everything out for you, and it's specifically for those of us who blog and post in message boards and forums. You can't organize your pictures as much at Photobucket, but it's so easy to use. And it loads a lot faster. At the moment, I only use Photobucket for pictures I want to share somewhere, and Flickr as an "everything" album. I also have a Snapfish album, which a number of years ago I opened to be my main online photo album. It's very similar to what Yahoo Photos was like, it's easy to manage your pictures and fun to use. It's free, but the only catch is you have buy something once a year to keep your pictures safe. They email you a warning a month or so before you're due to buy something, but if you don't check your email or have steady access to a computer, you may not get the warning, and one day you find your account no longer exists and all your great pictures are gone forever.
But you can buy something as little as a 12 cent print, so it's not too big a deal. I've been happy with them.