Eliminating the electoral college outright would require a constitutional amendment - an amendment which would never pass because Republicans, who rely on the small states to win, would never support it. (And the small states themselves would not want to dilute their own strength.)
So what about reform at the state level instead? Two states, Maine and Nebraska, award their electoral votes on a sorta-proportional basis. This year, Coloradans voted down a proposal to award their electors on a purely proportional basis. Either system, however, would not really eliminate all of the problems caused by the EC, and in any case, they'd both hurt Democrats.
Most other ideas run along the same lines and are either impractical or unsatisfying. But a reader at the Swing State Project once described a plan which I think might be viable. Nathan Larson pointed out that the Constitution (Article II § 1) says the following:
The meat of this proposal is on the flip.
If the eleven largest states - CA, TX, NY, FL, IL, PA, OH, MI, NJ, NC & GA - passed such a measure, 271 electoral votes (enough for victory) would automatically go to the popular vote winner. And to safeguard against states trying to stick with the old system, these laws could include a trigger saying they wouldn't go into effect unless states totaling 270 EVs have also passed similar measures.
Of course, I can imagine the outrage people might feel if their very blue state gave its electors to a Republican or vice-versa. But clearly, we'd just be talking about mere formalities - do you really care where your EVs were allocated if your guy lost?
The main obstacle to implementation would be whether the swing and Republican states on the list would go along - the swing states might be hesitant because they'd lose their coveted status, and the GOP states would (perhaps rightly) fear that this plan would hurt Republicans. My response is that the swing states - Florida, Ohio, Michigan , etc. - won't always be swing states, and they should plan for the future. And the states on this list which went red by sizable margins are all (except TX) trending blue.
Thoughts, criticisms and alternate proposals are - as always - most welcome.
Update [2005-1-7 16:35:35 by DavidNYC]: Drew in the comments observes that the Amar brothers (both law professors) discussed this proposal three years ago.