Yes, I frequently inject myself into the protagonist of games I am playing. It's an escapist fantasy for me, and I like pretending that it's me in that situation. Who "me" is might change, for example in games like Skyrim, where I can make any character I want, I will create a backstory for the "me" I am playing this time, and have his actions be reflected by that history.
Other games, where I don't have the choice, as there is one set protagonist, I just pretend it's me, and do the actions that I would do, to see how the outcome would be.
It's why I rarely play characters on an evil path, because I don't like doing shitty things to people. And since the character is an embodiment of me, it makes me feel bad.