Both Billie and Bob have given part of the answer. Here’s the longer version:
In the U.S., elections are done on a statewide basis, so it’s theoretically possible that a candidate for President can be on the ballot in some states, but not in others. Each state has its own requirements for getting on the ballot- usually a petition containing a specified number of signatures from registered voters, or of voters from a particular party.
While it is possible for a single person to scramble around and get all the necessary signatures, the requirements are sufficiently high that it is almost necessary for the person be affiliated with some sort of political party to provide the strength of numbers and organizational efforts to obtain the necessary signatures statewide.
Most states have four major political parties: Republican, Democrat, Conservative, although the latter often overlap with the former. In addition, many states have additional smaller political parties-- Socialists, “Right-to-Life,” Worker’s World, Libertarian, etc.-- that manage to get candidates on the ballot for some or all of the races in a given election. Few tend to win, however, because they simply don’t have the numbers behind them that the two main parties have.
As far as I know, each state allocates only one ballot position per race to a given political party. Therefore, in the race for President, the Republicans must pick one candidate to represent them, the Democrats must pick one, and so on. (In races where more than one seat is available, such as school boards or council seats, each party gets as many ballot positions as there are open seats.) Therefore, prior to each election, each political party has an internal election to decide which of several candidates they will run as their representative. These are the “primaries” that you see going on now. Nothing prevents someone who loses the primary election in their party from being selected as another party’s candidate-- for example, if McCain won the Republican nomination, the Conservative party might select Bush as their candidate, and both of them would appear on the presidential ballot in November. But typically, the strength is in the two major parties.
That being said, the popular vote in the U.S. doesn’t directly result in the selection of a president. Constitutionally, the president is elected by the Electoral College, which consists of several hundred delegates. When someone votes for president in the U.S., what they are actually voting for are delegates to the Electoral College representing their candidate. As far as I know, states are “winner take all” for delegates-- if Bush wins the popular vote in New York, all of New York’s E.C. delegates are appointed by him, and will (most likely) cast their electoral ballots for him. (The delegates are not legally bound to vote in the E.C. for the candidate they were appointed by, but obviouslly, most usually do.) A person must receive a majority of all electoral votes to become president. If there were a three-way split-- say because a third political party managed to win several states-- and nobody had a majority of electoral college votes, the top three candidates would be sent to the House of Representatives who would vote on who the winner is. Because the two main parties in the U.S. are so strong, no third party candidate has ever won a single state in a presidential race, so we’ve never had to even deal with this sitaution. Yet.
Because states are winner take all, it is possible for a candidate to lose the total popular vote but still win the electoral college vote. A candidate might win New York state, with, say, 30 electoral delegates by a single popular vote (let’s say 300-299), but lose Vermont, New Hampshire, Pennsylvania, and Massachusetts, who total, say, 29 electoral votes, by a landslide (let’s say 100-400). Since the candidate winning New York has more electoral college delegates, he or she will be the next president, even though 70% of the population voted for the other candidate. Weird, huh? It’s happened twice before: Rutheford Hayes lost to Samuel Tilden in 1876 by a few thousand popular votes but won by one vote in the E.C., and Benjamin Harrison split Grover Cleveland’s terms as president, even though Cleveland won the popular vote in that race by about 40,000 votes or so.
That’s U.S. Civics 101 for today. Read pp. 103-123 in “Land of Truth and Liberty” for tomorrow’s class. And remember, your term papers are due on Friday.