In the state of Oregon, all elections are conducted by mail, and have been since 1998. Oregon is currently the only state in the United States to use this system. (Washington will begin to use this system statewide in 2010).
The system works fairly simply: several weeks before the election, ballots are mailed out to all registered voters in Oregon. Along with the ballot, the envelope also includes an explanatory statement of the ballot measures, and a secrecy envelope, and a postal return envelope. The voter fills in bubbles for candidates and ballot measures that they support, as well as filling in write-in candidates if they desire. They then seal it in a secrecy envelope, and then put it in another envelope that they sign and return either by postal service, or by dropping it off at a designated place.
The system has been in place since 1998, when Ballot Measure 60 was approved broadly by the people of Oregon. Many of Oregon's ballot measures tend to be politically polarized, supported by either urban or rural counties, but Measure 60 passed by wide margins in all counties of Oregon. It seemed to have wide cross-partisan support, and in the ten years since, there have been no serious challenges to vote-by-mail. Also, as far as I know, there has never been any serious election fraud connected with it. Although wider voter participation is often considered to be of benefit to the Democratic Party, the convenience of Vote-by-Mail seems to be something that no one wants to challenge.
I don't know specifically why Oregon was the first to adopt this system, but I suspect it has something to do with what I take to be the large, complicated nature of Oregon ballots. Oregon still uses parts of the Oregon System, where some laws are left for the voters to decide. There may be a dozen of these statewide measures on the ballot a year, and the arguments for and against them may require extra time to decide. There is also a great amount of candidates in Oregon, with President, Senator, Representative, Governor, Secretary of State, Treasurer, Attorney General, Commissioner of Labor and Industries, Superintendent of Public Instruction, County Commissioners, Judges, Sheriffs, Mayors and City Council People all having to be decided on (and this is actually a partial list). Stuck in a voting booth, a voter may be likely to vote for the first familiar name as they get further down this list. With vote-by-mail, a voter can spend a weekend afternoon studying the candidates and measures, with the help of the (somewhat misnamed) voter's pamphlet, which is a hefty piece of reading, this year coming to two 100 page volumes of statements and explanations.
In the current election, one of the great surprises is the very high rate of early voter turnout. It seems that vote-by-mail is an idea whose time has come, and its success in Oregon may be a sign that other states should adopt it.