As you probably know, Bush can't get re-elected for a third term (unless an amendment is passed and that is highly unlikely). Here are the most suggested names for candidates, yet all of them have some serious difficulties to overcome for them to be a viable candidate. Usually when this happens, one or both parties usually pick a relative unknown who hasn't been damaged by national recognition yet.
Hillary Clinton (D) - The Junior Senator of New York has been suggested quite a bit. She has wide national recognition and her election would make Bill Clinton the first gentleman. However she is the most hated Democrat amongst Republicans. The South won't vote for her since she abandoned Arkansas for New York. A President can't win without some Republican votes and she's just too disliked by Republicans to win. She could win in a Democratic primary since Democrats like her, but it doesn't seem likely that she could win the presidency.
Barack Obama (D) - The new Junior Senator of Illinois will have 4 years in the Senate in 2008. While he is a very viable candidate in the future, he'll be too inexperienced by 2008. It's doubtful he'd acquire enough contacts in just 4 years to raise the necessary funds and support to become President. As seen at the Democratic National Convention, he is an excellent speaker, very likable and charismatic. However a first term senator has become President once before, so it is a possibility.
Al Gore (D) - By 2008 the stigma he acquired from the 2000 election may be gone. However he needs to become more personable and act less like a robot. If he runs a very strategic campaign, he could win like Nixon did in 1968 after being defeated in 1960. However he needs to play his hand aggressively and masterfully.
John Edwards (D) - He couldn't carry his own state for Kerry in 2004, so why would people support him? His wife has just been diagnosed with cancer, and that problem will take some of his time. However it seems doubtful that a losing vice-presidential candidate would make a viable candidate when history tends to forget them fast. However, he does have a lot of free time now since he gave up his Senate seat to run in 2004.
Howard Dean (D) - He crashed and burned when he acted like a monster truck announcer at one of his rallies. He will have a hard time living that down. He is also only a so-so fund raiser which hurt him in 2004. After the trouncing the Republicans gave Democrats in 2004, they'll probably be looking for a less liberal candidate than Dean.
Arnold Schwartznegger (R) - He'd be an ideal choice to win if it wasn't for a couple of things. He's ineligible to be president since he wasn't born in this country. A Constitutional Amendment would be needed and usually an Amendment takes at least 7 years to get passed since it's so hard to pass one. It seems unlikely he could be made eligible by 2008. He's also pro choice and slightly liberal as Republicans go, and so he'd have some trouble getting financial backing from many Republicans. However if he could make himself eligible in time, he's highly charismatic, very likable, and is widely recognized and liked by Democrats and Republicans.
Rudolph Giulianni (R) - An ideal candidate, since he has wide national recognition. However he's never held a top federal position, a congressional seat, or a governorship. He was just the popular mayor of NYC and a top federal lawyer. Most candidates usually have held higher offices before being a viable candidate. He's also pro-choice and very liberal for a Republican. He's balanced his pro-choice stance by saying that he's against abortion morally but while it's legal he will enforce that right if it's his responsibility to do so. His liberal stances may make it hard for him to raise money from Republicans, but many Democrats and Republicans like him. Bush could groom him for the presidential position by giving him a cabinet post. He would be ideally suited to being either Attorney General or the Secretary of Homeland Security. John Ashcroft and Tom Ridge may be leaving soon and he could fill one of those vacancies. However, while Guilianni was a very vocal supporter of Bush in this year's election, Guilianni may simply be too liberal for Bush.
Dick Chaney (R) - He has expressly said he doesn't want to be president. He has health problems and he's not very charismatic. While he has an impressive resume in politics, he's not seen as very likable.
Colin Powell (R) - He has expressly said he doesn't want to be president. He might have been a viable candidate in 2000, but he's missed his chance.
Jeb Bush (R) - He has expressly said he doesn't want to be president. He has a Mexican wife who people may not accept as a First Lady. However if he changes his mind, he could be a contender.
John McCain (R) - There's a question as to whether he was born in the USA, and is therefore eligible to be President. He was born in the Panama Canal Zone. At the time he was born it was US territory, but as of 2000 we turned the Panama Canal Zone over to Panama as Jimmy Carter originally put into motion. Therefore it's debatable on whether he was born in this country. His candidacy would therefore be open to a court challenge. Eventually it might reach the Supreme Court which is conservative and would probably vote in McCain's favor. He is very popular amongst Republicans and Democrats. However he is not a good fund raiser. His lack of fund raising skills hurt him in 2000. He is also not popular amongst the powerful elite in his party who consider him an outsider, and it was not appreciated that he challenged George W. Bush in 2000 and beat him in several primaries before he ran out of money. Republicans don't like their candidates being hurt in primaries and don't want to open themselves to the same weakness of a primary fight as Democrats do. If he can find a way to make peace with the Republican powers and find a way to overcome his fundraising weakness, then he might be a good candidate. However he will be 72 in 2008 and many people won't vote for him because of his elderly age (which hurt Bob Dole 1996).
Bill Frist (R) - His name is mentioned since he is the Republican majority leader in the Senate. However, top leaders in Congress are usually picked now for their moderate and quiet demeneor. Bill Frist isn't that charismatic and the duties of a party leader are extreme and do not allow him to take time off to fundraise and campaign. He would probably have to give up his top post to run and Republicans don't want to scramble for another leader if they don't have to. Republicans tend to discourage and punish infighters and those who cause infighting.
Do you have any names to add to the list?