Your webhost provider may offer hotlinking of images (which is what PhotoBucket and Flickr do) but I doubt you can fine tune the control so that only you can do it. I have hotlinking from my site switched off to protect my bandwidth - if someone were to link one of my images (maybe just to some innocent discussion forum) I'd be paying for their use of bandwidth, and that's not cool as one image downloaded a zillion times would bleed dry the monthly bandwidth you pay your host for.
Photobucket have always been a pain anyway since for some reason they disapprove of nudity. I'm one of their paying customers at £15 a year, but I think that will be stopping quite soon.
Edit: Actually I have so much stuff linked from there I probably will keep it for convenience, though that will disappear if they hike the price too much. Barrel, over, got me.