Given all the videos and comics they put out, it's kinda shocking that Valve never did this themselves.
Modder DrLilRobot recently put out a prototype of their Team Fortress 2 story mode. It's a little rough around the edges, but given that TF2 is meant to be a multiplayer class-based shooter, they have contorted it in some damn impressive ways.
Right now DrLilRobot is gauging interest to decide whether or not they will continue building out the project. Enticingly, they have said that a level based on the End of the Line update content Valve rejected, much to the TF2 community's chagrin. Here's hoping.
What do you think? If it was done well, would you play something like this? What would it need to be fun for you? Multiple ways through each level depending on your class? Dialogue options? Loyalty and romance quests? If the latter, I can't wait to make Heavy finally tie the knot with Sasha. Also I would pair Scout and Spy, because come on: something is going on there. Something ever so slightly oedipal, but mostly beautiful.