Range voting works like Olympic voting, with each voter giving a rating out of 10 (or any number), and the contestant with the highest average wins. This means that in politics we are able to express a range of attitudes towards candidates. We can also vote highly for multiple candidates, which allows the current two-party system to diversify into any number of parties that can be very similar but still successful. I believe this would be very advantageous to the future of America.
Another good alternative is Approval Voting. In this system, each voter can approve (or not) of each candidate individually. Each approval counts as a 'point' in favor of that candidate, and the candidate with most points wins. Some people may feel this violates the 'one person, one vote' principle, but really that idea is that no person should have more impact than any other. With this, it's impossible for anyone to give more than one point to any candidate, so the impact of each person on each candidate is equal.