I really like the idea of 'E-Sports' (but not the name) though I find the games played are mostly about twitch reflex and not strategy/tactics which I would consider much more interesting. Starcraft is one of the better options, but at that level tends to just be a micro-action-per-second-click-fest.

So are there games played competitively that involve using your brain? If not, what do people think would be a good candidate?

Might not be what you're looking for, but I'd say chess!

Is there a battlechess league?

I'm not sure but you can play board games like chess, checkers, backgammon, etc. for free at various sites on the web (Yahoo used to be a popular one).

I've watched and sampled a wide variety of e-Sports. Competitive gaming usually involves quite a bit of thinking; the best player is never the one who clicks fastest or has the most impeccable aim because at the very top level, the differences there tend to be minor and usually irrelevant.

My recommendation for a good viewer experience are StarCraft and Quake Live. StarCraft, when properly observed and casted, renders the micro and APM almost imperceptible, giving instead a dynamic game of harassment, tank lines, attacks and counter attacks. At its best, it is a true spectacle to behold. While this broadly applies to both StarCraft games, my sympathies and recommendations lie firmly with the old Brood War - nothing has come close to replicating the spectacle that it could provide. The one downside, to this and other strategy games, is that without a solid understanding of the game itself, some of the finer strategic decisions could be lost on you.

As to Quake, again good casting is key. But the duel game revolves around controlling the map and the various weapons and power-ups on it, keeping time on their respawning, denying them to your opponent. In my experience, the most gripping games of QL are the ones where there are barely any frags and the score remains 0-0, or 1-1 until the last seconds. These are games of cat and mouse, prodding attacks and timely retreats. There is a definitive advantage to not having headshots in your game and being generally unrealistic, and professional quake is the proof.

Hope this helps a bit, let me know if you're looking for more tips. Or something else :-)

This is a fair observation. I should acknoledge that there can be more to these games, but it still isn't what I had in mind. These are (to me at least) mostly about thinking on the spot and knowing the game/level rather than deleoping strategy as the game progresses. I suspect what I have in mind is more likely to be exposed in a turn based game, such as XCOM (though that may not be the best game for it). Another thing going against Quake Live specifically is knowledge - Video games have a big advantage over board games such as chess in that they can present limited knowledge to each player (ie: fog of war). This enables hidden strategy to play out (yes Starcraft has fog of war, but it doesn't hide much in terms of strategy).

I'm not sure I quite get you here, could you elaborate? Are you looking for less knowledge or more? For the two games, they both have a large aspect of hidden information. In StarCraft, scouting is essential to compensate for this, as is map vision and control. In Quake, a player can only be certain of his limited surroundings and is never completely sure where the opponent is - that knowledge must be deduced from the layout of the map and what the player believes his opponent is after.

As for TBS, I've seen some replays of competitive HoMM3. Not very captivating, and that's if you ignore the tedious and somewhat random buildup to the climactic battle.

http://tabletop.geekandsundry.com/

It's not exactly what you're looking for because it's not video games, but it maybe something you'll really enjoy anyway. TableTop over at Geek and Sundry is a show hosted by Will Wheaton, guest starring minor geek celebrities playing board and table-top games. Very very entertaining.

In the world of e-sports, I really can't help because I have the exact same mindset as you do, and I haven't seen it be done yet in an intelligent enough fashion. However, TableTop is people playing the game for their first, second or third time usually so you get to explore how they develop and evolve their strategies.

Spinorial: Maybe I'm just strange, sorry if I am not communicating my thinking clearly.

Gazoinks: Not angling for playing, just following. Particularly at an elite level.

vulchor: Yes, well aware of tabletop, seen them all.