Forget Florida just have Gore win any other state, New Hampshire and West Virginia come to mind, either state would have given him the needed Electoral Votes to be elected President, in fact it is believed if Gore did not just outright ignore WV while Bush spent money and time campaigning in the Mountain State, he would have won it. So Gore spends a couple of days in West Virginia making stops in Charleston, Wheeling, Morgantown, Huntington, and Beckley and narrowly wins the state in November.
Will 9/11 still happen? This can be argued one way or the other, but for the sake of argument lets say it does still occur, the US is thrust into a war in Afghanistan, and in spite of the neo-con rhetoric the US will be involved in Afghanistan. However will Gore win re-election? I doubt it, the US hit economic hard times after 9/11 and it is very likely John McCain (again for the sake of argument) runs against Gore in 04 comparing him to Clinton, in which Gore responds if Senator McCain wanted to run against Bill Clinton he should have done so in 1996. {Though being compared to Bill Clinton would only be bad in the eyes of neo-cons at that point}
However in 2004 McCain defeats Gore ending 12 years of a Democratic White House, and is fairly popular. Without the Iraqi war which I doubt Gore would have gotten involved in, the economy is doing okay in 2008 which allows John McCain to defeat Hillary Clinton in the election, Barrack Obama deciding not to run, and we get spared the nightmare that is Sarah Palin.
Already looking forward to 2012, pundits are predicting Vice President Fred Thompson will be a sure thing for the GOP nomination and are looking at Barrack Obama, and John Edwards as the likely nominees for the DNC.