Not sure what's best really... any thoughts? What's your preference grahame? My take is that images on this site are just for news or entertainment value, so it doesn't matter if they are lost after a fairly short time...
I host my own, and they're on the same server as the main site - though a different domain. I'm fortunate to have such a hosting setup, together with the background / knowledge of how to use it and the security that allows me to modify and add to what's there but should be pretty effective in preventing others doing the same.
We've said in the past (discussed 'behind the counter') that we are not a general image hosting service - we don't have the server resource nor the admin and management resource, all of which is donated / volunteered here. Instead, we recommend people to use third party hosting (I suppose I am my own third party). Attachments to posts provide a lightweight way of adding images - effectively as an appendix to a post, and only visible to members, and even then only when looking at the thread directly and not through the 'recent' tag.
Now - that's not ideal. I would prefer to host all the images that are within all the threads on this forum. That would save us the issues of images being lost when a hosting site goes away or changes its policy, and it would allow our team to provide somewhat more help as and when members need help. I disagree with Red Squirrel - it
does matter if the images are lost on what has become a valuable archive, but I'll have to admit that in the great run of things it's not exactly a top-10 problem. Not sure where I am going here ... headed off to do an experiment.