While we're all posting pictures of physical media, here's my progress approximately 6 months after I've picked up board games as a hobby:
It's not much of a collection, but it's getting there.
Agricola, Puerto Rico, Carcassonne + Inns and Cathedrals, Ticket to Ride, Pandemic, Battlestar Galactica, Munchkin, King of Tokyo, Galaxy Trucker, Game of Thrones Card Game, as well as the game that got me into the hobby - Zombies!!! + mall expansion.
And Cards Against Humanity because where else am I going to put it.
So far my favourite is Carcassonne - I think the art is gorgeous, the game is incredibly simple to teach, and I find the tile and meeple placement systems to be incredibly engaging and strategic even though there's a whole lot of luck involved.
I've only played it a few times so far, but I'm also really enjoying Puerto Rico, perhaps even more than Agricola.