Name one election, poll, or contest - anywhere - that utilizes the concept of down voting.
I have certainly seen polls that use the Agree/Disagree or Approve/Disapprove format. Such as "Do you Approve or Disapprove of the job the President is doing." Those types of polls are not at all uncommon. Selecting Disagree or Disapprove seems to me to be akin to down voting. I don't know how useful that type of poll would be, if the only option you had was Approve or Agree.
Also, there are those opinion polls where you can select from 1-10 wether you agree or disagree. Selecting 1 would also seem akin to a down vote.
I am not sure why people get so worked up about the votes. It isn't as though it affects your forum membership where you get a prize if you get the most up votes or kicked off the forum for accumulating a number of down votes.
One of the local newspapers here uses a Thumbs Up / Thumbs Down vote system on replies to articles, with a couple of differences that might be nice to see implemented. First, they tally and show both the up votes and the down votes. So instead of seeing a post that has -8, you would instead maybe see a post that has +6 / -8. I think maybe that is more accurate than simply the +/- number alone. Also when you look at someones profile, it tells you how many thumbs up and thumbs down votes you have received and how many of each you have given.
But again, what difference does it really make. It is all academic and provided for little else than interest and a little amusement.