My karma management techniques:

1) If I'm in a thread and someone's comment is rated equally with mine, and therefore potentially displaying atop my comment, I downvote theirs until it'll pass mine despite my downvote, to give my comment more exposure. I remove the downvote later, usually upvoting (their comment is getting voted better than mine because it's good).

2) If I'm debating someone and I want to downvote their comment, I upvote it for a day or so, then later return to downvote it. This gives the impression that two objective observers who read the thread later agreed with me. This works best on long debate threads, because a) if my partner's comments are getting immediately upvoted, they tend to be encouraged and will continue the debate, further exposing themselves to downvotes and b) they get fewer reads, so a single vote up or down makes a much bigger impression when almost all the comments in the thread are rarely upvoted/downvoted past +/- 2.

3) Karma is really about rewarding or punishing an author for content, to encourage certain types of content. Comments that are too aggressive will not be upvoted even if people agree with the point, because they don't want to reward aggressive behavior. Likewise, comments that are not aggressive enough are given extra karma - the reader's first instinct is to help promote this message because the timid author won't promote it enough on his own. This is nonsensical in this format, but the instinct is preserved.

I've noticed that the comments that get voted up the most are those that do probability calculations, those whose authors' names pop out of the page, and those which are cynical on the surface, possibly with a wry humor, while revealing a deep earnestness. If you have something unpopular to say, or are just plain losing an argument, that's the best tone to take, because people will avoid downvoting if they disagree, but will usually upvote if they do agree.

EDIT: I agree with Alicorn that votes shouldn't be anonymous, as it would remove the dirtiest of these variably dirty techniques, but in the meantime, play to win.