I've seen many photos from other websites like photobucket and flickr go away. which is annoying and it especially happens in older entries. They just don't work. I've never seen an image from imageshack that went away which is why I use them.
No offense Sandie, from this side I dislike Imageshack. It seems like photos from users hosting with them take three times as long to load as from other sites, almost as if their servers are severely overloaded.
I suspect the reason the Photobucket images "go away" is because it's so easy to move the photos around among different directories. You move them or re-name them, you change the URL and thus break the link. I try to resist the temptation of moving stuff in my directories as I know I've got many of them posted on forums.
Rex is absolutely correct, just about everybody has space available with their ISP although depending on what software you decide to use to upload your photos, you may need to be a bit tech savvy to do that.
Personally I like www.photobucket.com, although one thing they don't have which I wish they did is space for an involved photo description. Captions only. I believe that www.webshots.com does have that however.
I've been using Photobucket for quite a long time. I currently have 535 pictures and 7 videos (five over 30MB) on my account. The only time I have a problem is, of course, when the site goes down. Other than that it's simply copy and paste the image tags into your post and you have a posted picture!
Heck the oldest picture in there was uploaded the day after I graduated, nearly 3 years ago.