Which software/program is the best for downloading &/or converting YouTube Videos?

I have been told that there are many programs/software types/websites/etc. that allow you to download a YouTube Video & save it onto your computer, and also convert the type of file (i.e. change the video from whatever type of file it is on YouTube--or whatever other video sharing site--to a video type, or format, that allows you to utilize it for other purposes).

Basically, I have heard of "Keepvid", and I have seen someone use it by copying the address on the YouTube page, and pasting it onto the "URL" part of the Keepvid page, and it allowed him to download the video onto his computer by changing the type, or format, of video by giving him different options on which type of format to download it as (such as .mp4, .mgp [I think], and many other types of formats). Then it asked him how to save the video (i.e. "Save As"; as well as where he wanted to save it--"My Videos", "New Folder", etc.

My issue is that I cannot use "Keepvid" because apparently it is not a safe website, and my computer's security programs will not allow me to use it. And, I'm sure there is a way to allow this site to run, however, I would rather use a different site, one that does not appear to be dangerous to use.

So, if anyone can let me know of the best site, or a list of the best sites, to perform the above activities, please let me know.

I am not trying to do anything illegal here. I would just like to play with it to see how it works, b/c my friend, or "associate" rather, strongly suggested I download a type of software/program that allows this.

Thank you so much, in advance!!!