Well yeah, lost odyssey and kingdom hearts comes to mind.

Lee Everett from The Walking Dead.

I always get attached to characters if they're written well. Ex: Ellie/Joel, Lee/Clementine, Lucina/Chrom. Hell, even Tippi in Super Paper Mario. There's absolutely nothing wrong with having an emotional attachment to characters in any medium. That's what the writers should be wanting to happen.

Fly, rocket (sob)! FLY!

https://www.youtube.com/watch?v=gmmOKF6lDuQ

I always thought that was weird...though it's probably my emotional intelligence being close to 0.

what about those little pikmin ?

I try to latch on to at least one character in any given game. Makes it more fun.

I think most people do, just like with movies.

So, first i would say that looking at a "lets play" is not the same as playing the game. You will not put your own effort in dscovering these characters and their sub-stories aswell as working on maxing their gear and their stats, explore the world with them and generally interact with them.
If you are unable to imerse yourself in these worlds, be it games, TV or movies,then without any sort of intention to flame, you may have some psycological condition that prevents you from feeling it. I recommend seeing a psychologist if its something that you feel not only with entertainment but also real people. Those kind of conditions are well documented and i dont know what sort of treatment there is, but it might be worth checking out.

edit: Decided to delete this paragraph as i think it didnt deliver the message the way i intended it to.

Rarely... can't even remember the last game that did.

I do kinda feel bad for them when I hear them scream before they die lol