Photobucket is the easiest I think. After you upload the pic just copy the IMG link and paste it on here in your message and it will show up.

 

There is also a site called postimage.org

No registration, no nothing (unless you want to). Just upload, click on image for larger version, then click "show codes" and click the copy button for "direct link". Come back here, click the yellow "insert image" button and paste the link

 

sounds like new version of imageshack.us