Two part answer
i) Bush: The US constitution allows a person to serve as President for a maximum of 10 years. 1 Presidential term lasts for 4 years so Bush can run again in 2004 but not in 2008.
Even if he were to be re-elected and serve till 2008, he could not run again as a further term would take him past the 10 year limit.
Why have the 10 year limit when terms are 4 years? - It allows Vice-Presidents who become President via death/impeachment late in a term (i.e. with less than 2years to go) to run twice in their own right
ii) Gore - like any losing candidate he can run again as many times as he likes, providing the Democrats will hav him