I spend a lot of time on Youtube, perhaps too much, but thanks to these channels I can at least feel like I'm learning and growing from that time. They all engage in fun geekdom and can educate as easily as entertain, although some are included here for raw entertainment value.
1. Channel Awesome
Name aside, this channel is actually really awesome. It is home to the Nostalgia Critic and several others. The reviews are part comedy skit and hugely entertaining.
2. Comicstorian
If you enjoy the characters from Marvel or DC movies or shows, this is a great channel. The theatrical readings of comic books are enjoyable and I often put them on in the background when I'm doing something else. Hearing more of comic book lore is a lot of fun and this channel updates frequently.
3. Crash Course
Hank and John Green are amazing people with so many projects I can't even begin to list them all. This, however, is one of my favorites. These videos are, as they say, crash courses in a huge range of topics. If you have a specific question you can skip to the one you want, or maybe you just feel like hearing about a topic from fun people with amusing visuals.
4. Film Theory / Game Theory
Two channels from the same creator, so it feels like cheating to separate them. These channels take elements of TV, movies, or games that people can wonder "how is that possible" and aim to answer that very question. Full of great information and jokes, I'm never bored even when I don't know the source material at all.
5. Cracked
The videos from this channel almost never fail to be amusing and are frequently educational as well. Think Buzzfeed, but with more educational value for equal amusement.
6. ScrewAttack!
I love this channel, largely for the Death Battle series it features. They don't come out very frequently but are always worth it when they do and the channel has plenty to offer between them to be worth watching.
7. Team Four Star
Easily my favorite, DBZ abridged is a hugely entertaining series that I find myself watching over and over and still finding funny. Even if you never watched Dragon Ball Z or didn't like it, give this series a try. They also do gaming videos and have done some abridging of Hellsing that can be quite entertaining.