Is The Last of Us Going to Have Multiplayer?

It's been confirmed The Last of Us will have multiplayer. Creative Director Neil Druckmann confirmed it a while ago in an interview with Gaming Examiner:
We are supporting multiplayer with The Last of Us. We’re not ready to talk about the details of how multiplayer will be implemented, however we can say that it is not co-op within the main campaign.
- Neil Druckmann

Furthermore, Arne Meyer(Naughty Dog Community Strategist) announced a bunch of stuff for the game including bonus content you can unlock for pre-ordering the game at GameStop.
Bonus experience points for multiplayer, A multiplayer melee attack booster, Some extra starting in-game cash, Special customizable character items for multiplayer, Two special bonus skins for Joel and Ellie which will be unlocked after your complete the single player campaign

What kind of Multiplayer Modes will be in The Last of Us?
As of now, no one knows yet. but judging by Naughty Dogs past creation, the Uncharted Series, you can expect something similar to it. Of course with it's own survival spin. Some people have come out with their own ideas of what Naughty Dog could be cooking up. Here you can read PlayStation Universe's thoughts on what could be "the best multiplayer in years."


The Last of Us Box Art

Arne Meyer also confirmed in the comments the final box art for The Last of Us: