I recently got A Game of Thrones LCG (3x core sets) and I'm just playing on my own to work out what the rules are.
I played Martell vs Night's Watch, and while Martell has some great character cards (Doran Martell, Red Viper), The night's watch's The Wall card is super OP, 2 Power each round and Martell's only shot is to get a card that removes locations.
I also played The Castles of Burgundy card game, and while I have the board game, I haven't played that yet, but the card game is really fun and very portable, I recommend people check that out.
Finally I picked up a few games in the last couple of weeks due to sales. Cacao (my only other tile laying game is Carcasonne). Concordia Venus, got a really good deal on Amazon.co.uk that was too hard to pass up. Troyes, another deal, and I love the art work in this, I didn't realise the game was a bit like Caylus. Game of Thones LCG Wolves of the North - I'm slowly grabbing a few of the deluxe expansions, I don't know if I'll get them all, but I'll definitely get Lannister, and maybe Night's Watch, Baratheon.
Also Arkham Horror LCG Core Set is really hard!