Do PC games need a running Internet connection to play the single player?

Most games only need the internet connection for the initial registration/activation. After that you can play them offline. Mass Effect 3 is one example of a game that unfortunately does need an internet connection at least when starting a game since it does an online DLC check every single time. Despite what the answer directly above mine says, Ubisoft actually removed the always online requirement from all but 2 of their titles. AC2 no longer requires constant internet connection.

That will depends on each games and how the developer/publisher implement the system. Like Diablo 3...you need to have internet the whole time while playing the game and activation. As opposed to Torchlight 2, which used different philosophy. No internet is needed to play at all. So it's up to you to find out how each game's implementation. Of course, your comfort level. I have use both and does not matter to me...but it is nice to play a game on a laptop, without constant internet connection while you're away from home.

you generally need an internet connection for games like WoW minecraft, guildwars it's better to have one tbh