Is taking a snapshot of the virtual machine that a VPS runs on a standard feature provided by VPS hosts?
Well, it depends on what you mean with snapshot. Do you mean an image of the OS, or a backup?
Some VPS providers offer images and/or backups, and some don't. It's not 'usual'. I have used one VPS host, they gave me a free backup server of 50 GB. I was considering switching to another provider, they didn't offer backups but they did offer snapshots (images).
I also want to note that most VPS providers offer backups instead of images.
To answer your question: no, not typically. At many VPS providers, backup space is an add-on, but it will cost you more. Some VPS providers do the same for images.
The term snapshot can mean many things to many people. If you mean a backup, they should be doing that already and you should be able to do this yourself too. If you mean image backup then that would have be to asked of the ISP as to whether they perform image backups or not. Image backups usually mean having access to a server with a bootable floppie or cd-rom but there may be other options out there that I am not aware of. VPS would not normally afford this option except perhaps at the ISP level.
It has been a long time since I performed an image backup. I used to use Ghost since it was the best at the time. There are free image backups out there as well as regular backups that you should be able to use including free backup software available depending upon the linux install you have.