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Not out yet, but definetly it's worth a look:
I haven't played it, but Infinity Wars seems to have a client.
Then there is Magic the Gathering Online.
(click "download current version" not "download wide beta version" because the wide beta version sucks). This is probably my all time favorite game. The most popular formats are very expensive, but there are other formats which are very cheap and still just as fun/strategic/etc as the expensive ones, the main one being pauper. So it's cheaper and you don't miss out on any of the skill or fun.
The "current version" client has a play free trial button you can press on the log on window that will let you play with demo decks against other people (no registration of any kind whatsoever required). Although you shouldn't do this until you know how to play (the rules and general mechanics) since you can only play other people (there is no computer AI). If you really want to learn magic though then the best thing is to have someone teach you or short of that, buy Duels of the Planeswalker 2014 on Steam. DOTP lets you play against a computer and maybe other people as well. This is a great way to learn the game.
Next is Solforge which you can download and try for free through steam. I didn't care for it but i could see how many people would like it. It can be a completely free game if you don't mind grinding the packs. Some people complain of it being somewhat "pay to win" since the people who buy the good packs crack the good cards which you won't have unless you open packs too.
Spectromancer is an older one. I don't know if this game has any kind of community. I tried it once and it seemed okay.
I think there is another online TCG that has to do with World of Warcraft somehow, but I don't know what it is or if it's still alive or whatever. Upon further research I think it's called Hearthstone: Heroes of Warcraft, and I still know nothing about it.
Card Hunter is browser based and is played out on a map like a board game, but there is a card element to it. I played it for a week or so and it was okay. It takes a few days to be accepted into the beta.
There's another game kind of like this on steam called Prime World: Defenders. I never played it, but some people really like it. It's a mix between card game and tower defense I think.
Yet another one I haven't played is Might and Magic: Duel of Champions. I don't know if it is browser only.
Here is a list with some games I didn't think were worth mentioning: