The best idea I've seen yet is to do paper ballots that are counted electronically. Voters get a receipt with a confirmation number on it that will be published in an official count. It's totally anonymous, but you can verify that your votes were recorded correctly.
If you find that a vote is wrong, you raise the issue, they go back and check the paper ballot and revise the official count. Rinse and repeat as necessary.
It accomplishes counting the vote quickly and still protects the integrity of our elections better than what they are doing now.