According to a Canadian retailer, 18 NHL clubs have confirmed third jerseys for the coming season. I will not divulge my source here because this is just for fun and no one needs to be losing their job over it. If you're skeptical, there's nothing wrong with that.
Anyhow, with the disclaimer out of the way, below are the teams with "confirmed" third jerseys for next season, in alphabetical order.
Obviously there are discrepancies here from earlier rumors involving the Pittsburgh Penguins. The last thing we heard, by way of the Tribune-Review, was that the club was seeking permission to get third jerseys featuring the powder blue design worn at the Winter Classic in January. Either they were denied by the league or the information I have here is incomplete.
Now, aside from the Pens, this list meshes perfectly with the big list I posted a month ago. I suggest reading that post for information regarding possible design rumors that have been floating around.
Rumors: The Big List | All third jersey news
If pictures become available prior to official unveilings, I'll be sure to have them posted for your perusal.