Who is the President of Earth? What is this person's name? (At the end of Season 4.)
The length of a term in the future would appear to be 12 years, since Nixon was President from 3000 to 3012 and there was no mention of other elections during that time. There were a couple of brief interruptions in his leadership, though:
The First president seen in futurama is President McNeal. The Omicronians invaded earth and demanded (Jenny) McNeal, star of the "Single Female Lawyer" show. With the name confusion, Earth Politicians handed over President McNeal. He was killed as he wasn't the McNeal they were looking for.
This leads to Richard Nixon's head running for office and emerging victorious. He remains president for most of the series.
At some point in the series, The Omicronians invade Earth again. Nixon forfeits the presidency to the Omicronian leader, Lrrr.
Chris Travers challenges Nixon in a presidential race and wins, but because of a time paradox, fades away from existence during his victory speech thus making Nixon the winner.
So to answer your question, most probable that Nixon was and will be the series' president.