According to Robert Dahl's landmark book On Democracy, free and fair elections are one of the primary tenets of a true democracy.
This may be a bit on the nose, but free and fair elections are vital to a democracy for a number of reasons: they insure that those who govern have earned the consent to do so, and also they ensure from time to time that the people have a direct say in their government. Perhaps the most important reason that free and fair elections are important to a democracy, however, is that any person who meets the qualifications can run in the election and have the opportunity to make their voice heard as a candidate, and possibly as an actual member of the governing party.
Despite these healthy ideals, the concept of "free and fair elections" is not without its caveats. I will primarily focus on U.S. suffrage and election procedures, but many of these facts and principles have applied in electoral processes throughout the world.
When suffrage was first introduced into the independent United States, it was limited to white male landowners over the age of 21. While the white and male could be argued as specious and prejudicial (even in a time when only white males were presumably educated and in the know enough to vote intelligently, this was a rather backhanded idea, and only perpetuated such peculiar evils), and the age was a rather arbitrary limit bestowing power and responsibility, the concept of owning property was not an unimportant factor in determining who could and could not vote. Much like Alexander Hamilton's proposal that only landowners could serve in Congress, this aristocratic procedure served as a safeguard from those without property, who many rich men in America felt would start a new revolution. Their fears were not necessarily unfounded (witness Shay's Rebellion), but by the mid 1800s, virtually all property requirements for voting had been abolished, and had instead been replaced by a poll tax to ensure that those voting had a vested interest in the results of the race. This, of course, broke the first premise of the concept "free and fair elections."
After the Civil War ended, and blacks were given the right to vote, the South reacted by drastically increasing the rates of their poll taxes and also instituting literacy tests, required for a person to vote. Since many of the white men in town could not afford the tax or pass the test, either, they were grandfathered in. This disenfranchised many black voters, and certainly violated the "fair" clause of the free and fair elections principle.
To make matters worse, the 15th Amendment only gave rights to "citizens", and a string of court rulings in the 1880s denied citizenship to Native American and Chinese immigrants, and most importantly, rescinded suffrage rights given to women in the western Territories. As early as 1883, women were given suffrage rights in America, but it took nearly 40 years, finally requiring a Constitutional Amendment to give women the right to vote. Meanwhile, literacy tests and poll taxes were still in place, and soon afterwards, laws were passed banning Japanese, Filipino, and, for a time, Russian immigrants from becoming United States citizens. Native Americans were gradually allowed to become citizens, but were often denied voting rights all the same, in direct violation of the 15th Amendment.
Finally, in 1952, the Walter-McCarran Act lifted the ban on Asian immigrants' citizenry, and the final stage was set for the civil rights movement that dominated the 1960s. The Voting Rights Act of 1965 effectively ended the use of literacy tests in the South, one year after the poll tax was snuffed out by the 24th Amendment. This, coupled with a few court rulings affirming the laws, effectively ended most of the legal barriers to registration and voting in America. In 1971, 18 year olds were given the right to vote in the 26th Amendment.
I'm hoping someone will come along and amplify this rather nerdy writeup with their vitriol about how the 2000 election was stolen, or why no election is free or fair.