Hum, some might say this is a grey area considering copyrights.
So to try and clear some if not all of that up, any video uploaded to Youtube within the public domain of that hosting site, does mean certain aspects of copyright have automatically been waived as the video is available for public and free viewing.
Therefore DRM cannot apply at least not in full.
However any or all recordings done of any publicly viewed video must only be for your own private use and not for any monetary gain. Trying to sell any recording of something available for free is likely to cause some problems as well as being a bit silly, as who in their right mind is going to pay to watch something they can already view for free on Youtube itself?
The owner and publisher of that or those video's is likely to demand some compensation if you did manage to sell it.
So, to record anything for your own use and not for sale elsewhere is usually quite OK and comes under the fair use parts of the copyright laws in general.
Having said all that, there are a few trust-able and downloadable for free software's available.
Youtube Downloader being one which is safe in itself, however you should be careful during the installation that you remove ticks to prevent unwanted junkware being inadvertently installed alongside the program you want.
Another program available that is mainly a video converting software, which does also include a means to download video's from most video hosting sites, and also convert them to a large number of different formats at the same time, which is called AVC. (Incidentally Youtube Downloader will also do some conversions as well)
Both are known to me as being safe to use and do not contain any form of malware within themselves if downloaded either direct from the creators own websites or well known safe download sites. The only proviso being to be careful of removing unwanted extra's during download and installation when obtained from some third party download sites.
If anyone knows of any part of the above regarding the copyright aspect of downloading video as being incorrect, I don't mind being corrected as I am no expert or qualified copyright legal expert.