Help a furriner here. As I understand it, in America as in the UK anyone can stand for election to any post with a sufficient number of seconders. How would an election for the Presidency operate if a large number of people stood for the office? Say 1000 people stood. How would the ballot paper be organised?
In the United States, elections are run by the state governments, so the situation will be slightly different in each state.
In Minnesota, my home state, I believe the rules are as follows:
The candidates of “Major Parties” are listed first, in reverse order of the number of votes each party recieved for the race for that office in the preceeding election. “Major Parties” are defined as political parties that have recieved at least 5% of the votes in a statewide race in the preceeding election. There are 4 Major Parties in Minnesota: the Republican party, Democratic Farmer-Labor party (DFL, or the state’s version of the Democratic party), the Independence Party (strangely enough, this party does not advocate secession), and the Green party. In the last presidential election, the results were 1) DFL 2) Republican 3) Green 4) Reform (which has since changed names to the Independence Party). So, the names of the Major Party candidates will be listed in this order: 1) Reform (if they have a candidate for President) 2) Green 3) Republican 4) DFL.
“Minor Party” candidates, or everybody else, are listed in a random order after the Major Party candidates.
Each state has different rules regarding this, however. An example is the recent California recall election. This election had well over a hundred candidates for the Governorship. California’s Secretary of State created a randomized alphabet (s, h, b, m, etc…) and all the candidates were listed in the order of that randomized alphabet.
Other than being the nominee of an “established” party, just about anyone could get on a state ballot or two, if they were willing to cough up half a year’s income.
The state requirement vary to almost nothing to very significant in the number of signatures and you can hire people to collect the voter signatures.
In a typical presidential year, there might be 20 or more candidates appearing on at least one state ballot, but many of these would only appear in a few states.
Last time there was a dude called “none of the above” in a state or two and pretty much beat all the splinter candidates.
In New York, there is a long list of requirements you need to meet if you want to get on the ballot and aren’t an established party (defined as one that got 50,000 votes in the previous gubenatorial election). You have to get a bunch of signatures on your petitions, and the rules are deliberately complex and arcane (once, a candidate from around here was disqualified because he submitted the petitions 8:00 a.m. the day of the deadline – the law specified 8:30 – and plenty have been disqualified for using staples instead of paper clips on the petitions).
If someone 1000 people managed to qualify (I don’t think the numbers allow this, since you can only sign one petition), then all the candidates would have to be on the ballot somehow.
Well, in the U.S., instead of “standing for election” people “run for office,” which is much more strenuous. 
In Minnesota, Major Party Candidates are automatically printed on the ballot. Minor Party candidates have to present a petition to the Secretary of State listing the name and address of the candidate, the office he or she is seeking, and the signatures of eligible voters. For statewide races (President, Governor, Senator, Attorney General, Secretary of State, etc) one needs to present 2000 signatures. For US Representative, 1000 signatures, and for State Legislature seats, 500 signatures. An eligible voter can sign the petitions for multiple candidates.
In the state of Wisconsin, independent candidates for President or Vice-President of the United States must file nomination papers containing at least 2,000 and no more than 4,000 signatures of Wisconsin electors. These nominations papers must circulate no earlier than August 1, 2004, and the deadline for filing the papers with the State Elections Board is September 7, 2004. (The election is on November 2, 2004.)
As people have said, you can’t just declare you’re running for the Presidency and automatically get on the ballot. This is particularly relevant now that Ralph Nader has put his hat into the ring as an Independent.
Each state has requirements for getting onto the state ballot, usually either a set number of names on a petition or a specified percentage of a party’s vote in a previous election. These rules are made by the state legislatures, which are near universally comprised of Republicans and Democrats. In many, perhaps most, states, therefore, they deliberately try to make it difficult for other parties and for independent non-party candidates to get onto the ballot.
The established small parties - Greens, Libertarians - at least have organizations extant in all the states who can call upon their members to go out into the streets and gather signatures on petitions. Even smaller parties and independents have to find volunteers to do this or have the money to hire firms that will supply gatherers.
They also need knowledgeable lawyers in each state, because there are a mass of nitpicking rules about the validity of the petitions, down to whether they can be stapled together or not. Virtually all petitioners have to gather many more, usually two or three times more, signatures than the minimum required because they know they will be challenged by the Republican and Democrat lawyers who will try to knock as many names off the petitions as possible so that they fall below the minimums.
So there will never be a Presidential ballot with more than a couple of dozen names on it.
The recent special gubernatorial election in California did have hundreds of names because of the oddity that the petition numbers to qualify were so low. They developed special ballots for the purpose to fit the various voting machine types they have, and also rotated which names were placed in which order so that the known effect that the first name on a ballot gets more votes wouldn’t be a major factor.
P. S. You can, legally, always write in the name of anyone in any Presidential election, but that’s not going to get a candidate very far. The vast majority of the people who say they are running for President never get on any ballot at all, and have to rely totally on write-ins for votes.
In case anyone’s interested, in New York, the major parties that the State recognizes are: Republican Party, Democratic Party, Conservative Party, Working Families Party and the Independence Party.
Due to a recent court decision, New York is now required to also provide a space on voter registration forms to write in a party if you want to register for a minor one (Libertarian, Green, etc.)