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.
-hh