Can VLC crop black borders on the fly?

If you press C it will toggle through the crop ratios and may help you with eliminating the black bars.

Well, I should have checked VLC's Video menu as I did while posting this question... There's the crop to 16:9 option I was looking for... Anyway, if you find an automatic cropping estimation method, the bounty will still be there.

Simply go to VLC Player preferences > Video (you must be in "All" mode, not "Simple" mode). On the right-hand side, scroll down to "Video cropping" and type in either "16:10", "16:9", or "4:3", depending on what your screen's aspect ratio is. Press the Save button at the bottom.

If black lines remain, then they are actually part of the video as opposed to just an empty section of the screen. In this case, adjusting manually is the only logical option left.