Thought I'd just list the LCGs that I've had a chance to learn and play.
Dominion
Thunderstone
Ascension
Quarriors
Puzzle Strike
Trains
Android: Netrunner
I'm assuming that both Quarriors and Puzzle Strike belong here, despite not using actual cards. Perhaps I'm someone mixing "deck-building game" with "living card game", but I think there's at least a very large portion of games in either category that fit in both categories.
Anyway, I supposed I'm biased due to having spent years of my life reading about and playing Dominion first, but none of these other ones grabbed my attention the way Dominion did. Many of them just feel like Dominion knock-offs, and while playing them (especially Trains, Puzzle Strike, and Ascension), I can't get out of a Dominion mindset; still referring to the equivalent cards as Silver, Lab, etc.