It depends. For things like posting in critique forums and stuff like that, no borders. If you're posting the images in an online gallery... it's kinda tricky. A nice, elegant border can make a solitary picture stand out, however to look at a page full of pictures with borders is annoying. The way I see it, when you're working with pictures online, you have to think about the overall layout of the page.
As for printed pictures, a border printed on the same paper as the picture is absolutely horrendous. Please don't do it. Frame your picture, or mount it, or both, but printed borders are just plain bad in my eyes.
Either way, you need to make sure whatever you do doesn't take away from the image itself. If you're posting the image for a critique, don't post a border. If you're posting the image to show off in a blog or portfolio, go for a border so long as it fits in with the overall theme.
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