Does anyone know if this is considered a backlink in SEs' definition of a backlink. What i'm saying is instead of using a URL link, I just put a picture or an image that is coming from my site/server. Does this work as well? Thanks.

Well, if you link the image back, it might.

No. It just hogs the other person's bandwidth.

The only positive that can come from it pertains to sites who rely on images to sell their product (e.g. my silk wedding flowers client.) Brides in forums often hotlink the images to show how pretty the flowers look, and it can lead to the odd customer.

So would this pose a problem for forum moderators when they find out the link is not from their own site? I ask this because I use images alot as part of exchanging daytrading ideas. The problem of course as you mention is bandwidth hog. But I don't plan to spam the site, these posts are legit posts.

So the answer is no? They are not considered as backlinks in SEs guidelines?

It's not a backlink unless it's a link. Having a url appear in the page, Either in an img tag or plain text URL, isn't a link and wont be followed.