My garage door opener finally died. Are there any out there that work natively with Smartthings out of the box?
Not “natively” but the MyQ stuff is community supported 
That’s what I thought. I currently have the MYQ accessory installed on my current opener. Should I upgrade to an opener that has built in WI-FI (Any advantages to this?) or stick with the same model and keep using my MYQ accessory?
I installed a Liftmaster 8500 last year. If you have a sectional door, there is no better. Official support has been announced (how’s that coming @ben), but what I’m using works great.
Want it integrated? Or not? Choice is yours 
Chamberlain MyQ with battery backup with the horse power based on the size of the door. 1/2 HP was enough for my single car garage door. It never fails and had it installed a year back when we bought our first ever house. But it’s internet gateway too. Earlier had a horrible vintage craftsman from the previous previous owner.
SOMMER Direct Drive (I think an European brand) makes some real sexy garage openers. I nearly bought it but the installer said they can’t do it for some reason as they were not comfortable as they had never heard about it. Does not integrate with ST but as such I do not rely on ST plus my garage door even though it is set up.