it's the usual route, and yahoo and many others will give you free space for no cash. Russ hosts the odd avatar or two as I recall.
Edit: you could even use ebay to post a pic for a never-ending sale item, then link to that. Or any use one of the free photo sites that exist and so on. But Yahoo is probably easiest. Just make sure that the site does not require the viewer to log on: if it does, the image will not show on RHP
most broadband isp's (internet servicer provider) offer you free webspace (and even some dialup ones), you could use your own webspace, or if you have broadband you could host your own website (would have to leave your pc on tho! - your isp webspace would be a better bet). Failing all that like the others posts mention there are a lot of free ones, just google for them if you want a list. . .