Personally, I dislike Let's Play videos, especially because a lot involve someone being loud and annoying trying to crack 'jokes'. However, I do like developer commentaries as they provide very insights into a games creation, and may talk about cut features and what could have been. With the increasing popularity of Let's Play videos, we actually have gotten some interesting developer Let's Plays over the last couple years. These are a few of the developer and creator commentaries that I like.
Conker's Bad Fur Day
https://www.youtube.com/playlist?lis...ZWUEV0vaSL4rHf
(older NeoGAF thread)
A few of the ex-Rare staff get together to talk about the creation of the game. It's fun and relaxed and features a lot of swearing.... would you expect anything else from Conker?
Wolfenstein 3D
https://www.youtube.com/watch?v=amDtAPHH-zE
(He starts playing 8:44 in, but it's a good listen anyway)
John Carmack reminisces about the game with a lot of interesting insight and commentary, from gameplay to tech. It's more serious and technical than the Conker one, and he only plays for about 15 minutes, but it's still quite a treat.
Bayonetta
https://www.youtube.com/watch?v=EwvSd4kcfdk
Hideki Kamiya talks about Bayonetta for over seven hours. As he's doing it solo it does drag on a bit but it does give some insights into his favourite games.
Day of the Tentacle
https://www.youtube.com/watch?v=qumYnE2wYhA
Tim Schafer talks about this point and click classic. He is an interesting guy to listen to and his humour is pretty awesome!
These are a few of the commentaries that I like. If you have some that you like please let me know!