My own web site.....
Its always better to have your own site rather than using an image service or a free service as they are not always the most stable of things.
They go down and also don't provide any service contract.
ImageShack is good for short term images, like posting on a board or showing your friend. But I wouldn't recommend it for a regular site. Once the site gets popular they'll take the image down because of bandwidth.
I use imagecave, I think its the best, but if you upload huge files then imageshack might be better. Imagecave only allows i think about 10mb for each account.
I use my own site. Because if using a free service they take it down for bandwidth and then you get stuck with a ugly sign on your site pointing that out. Plus it's not stable
For big images I don't want to waste my own bandwidth on, I usually use ImageShack or Photobucket. I don't post images that gets too many hits, so I've never had a problem with them running out of bandwidth and gets taken down.
i use photobucket, I have from the start, they have a good amount of space that you can use for free and they provide you with links with codes and stuff with them.