For photo's, do you take the time to put your photo into an extra application (e.g. Photoshop) and give it a nice little border? Or do you just upload it as is? (Including any adjustments made)
I don't add borders to photos that are part of a group; but I do add them to individual photos being used as part of a web page (much, not all, of the time). However I generally use simple borders that are put in place with CSS rather than modifying the image.
I often use borders, drop shadows, and cut-outs to provide contrast to a whole image or offset portions of an image for emphasis or effect. Many examples on my flickr site (link in signature, below)...
It really depends on what you're doing and what impression you're trying to achieve. Generally, for webpages, I rarely use borders, but for prints to hang on a wall, I invariably frame them with matts.
For example, all photos had borders back in the 1960's and earlier. As such, if you're trying to reproduce a "period" look (particularly with B&W), then you'll want that on a webpage or whatever:
Similarly, sometimes a shot can benefit from sort of added border by creating a contrast:
When you're only spending electrons, it pays to experiment.