As per Todd's comment, both of these performers are doing 'live looping', using equipment that you could broadly describe as 'loopers'.
Reggie Watts is using the Electro-Harmonix 2880 Super Multi-track Looper.
I'm not sure what beardyman is using in the video, but there's an article here about the development of his setup.
It's very hard to recommend specific models, because every performer might need something different from a looper. I've seen some performers create intricate masterpieces using simple loopers, and then there are those performers (like beardyman) who can't find anything off-the-shelf that works for them. I can only recommend doing some reading around about current models of looper, and try to get hold of one for a price that allows you to flip it for something else for not too much of a loss if it doesn't work out (i.e. possibly second hand!).