Q: Say there's some music video on a certain DVD that my kid really like, and I don't trust my kid to load the DVD each and every time. Can I rip just the music video onto my PC and give them a shortcut to play it each and every time?
A: Absolutely! However, this is technically illegal and a copyright violation, but we COULD argue that you're simply... exercising your right to a backup as you're not using both copies simultaneously. So, here goes.

First, insert your DVD into your PC's DVD drive.
Second, you'll need to download "DVD Decrypter". I can't give you a link, but it's easy to find if you use Google. Download it and install it.
Third, run DVD Decryptor, pick IFO mode, and read the DVD. It should give you a list of all the different "VOB" files on the DVD, which are the actual video contents. The long one is probably the movie, and the short ones are the music videos. You'll need to try a few to get the right one, or pick rip them all.
Fourth, pick the right VOBs, and extract/rip appropriate ones to your HD.

The VOBs can be played by most media players, including BSPlayer, but if you want to go one step further... Use a converter to "transcode" it such as DVDx (which will transcode from VOB to MPG) or any other tool you want, to create the ultimate result. Enjoy!