I do both, at least in the context of linking say screenshots to others.
If I'm linking a very "casual" or non important screenshot then I'll just toss it up on my server and link that copy.
If it were somewhat important, then I'll upload it to my server and imgur and link the imgur copy, just in case my server goes down - doesn't stop imgur from deleting it either but if I get hit by a train and am made unavailable then imgur is probably the best bet.
If it is critically important then I try to avoid screenshots / pictures all together and just describe it in text because that has the best chance of persisting. And if the text disappears, then at that point the image is probably not as useful either.