As a resident of rural America, I'd like to keep the electoral college around. If we ditch the electoral college, do you think the candidates will bother to spend time stumping for votes in the smaller states or areas with low populations? Naw, they'll spend all their time campaigning in New York City, Los Angeles, Chicago, and other similarly colossal cities, 'cause that's where the most voters are. Why waste time in Nevada, Alaska, New Mexico, Wyoming, or any of the more rural parts of the country when there's so little benefit to be gained, right?
Of course, with zero attention paid to rural areas during presidential elections, the quality of life in those areas would drop. Why bother sending federal funds to sparsely-populated areas when there's no political benefit to be derived? The population of NYC and LA dwarfs the population of most Western states -- why not close their WIC offices and use that money to improve benefits to the poor in the Big Apple and Southern California? The votes lost in the West will be more than made up for in New York, and since all that matters is who gets the most votes, who cares about those rednecks, right? If they were worth anything, they'd move to the metro areas where their votes would count, right?
The electoral college may be a leftover from old constitutional battles, but it's the only thing that gets the candidates out to see what things are like out here in the sticks, and as far as I'm concerned, it's the only thing that keeps us country mice from slipping down into the Third World nation status that urban America seems to expect of us...
UPDATE: February 2021:
On the other hand, what we believed back in the day can be shown to be entirely wrong in the present.
As the last few elections have solidly proven, the Electoral College is not a good way to determine who wins elections in a democracy. The United States is the one of the very few democracies that use anything like the Electoral College. In most nations, it all comes down to whoever gets the most votes.
Heck, even at the local and state level in America, there's nothing like the Electoral College. Did your candidate get the most votes? Then he's now your city councilman or your senator or your governor. But for the presidency, we insist on using a system that was designed to appease slave states, and which has been shown more than once to prevent the winner of the popular vote from ascending to the presidency.
As for my old arguments about the Electoral College forcing candidates to campaign in rural or low-population states -- well, it doesn't really happen. Is there any reason for a candidate to campaign in South Dakota vs. Texas? South Dakota has three electoral votes. Texas has 38 electoral votes. If you want to win the presidency, the Electoral College very much requires you to focus your attention on Texas -- and New York and California and Florida and Pennsylvania and Illinois.
The Electoral College should be abolished. The only reason to keep the Electoral College around is if you're the Republican Party and can no longer win honest elections.