The Denver Post's blog "Politics West" makes one of the strongest points in favor of the electoral college, which is that it dramatically reduces the likelihood of a Presidential election that can only be resolved with a national recount. There can still be very close elections that aren't resolved quickly, as was the case in the 2000 election. But, even then, only one or two states will hang in the balance, narrowing the scope of the dispute. Also, vote counting disputes in close elections only really matter if they occur in states which will tip the electoral college balance.
Prior to Bush v. Gore, it wasn't obvious that the federal courts had a role to play in vote counting disputes at all, and there is still basically no way for voting counting disputes in multiple states to become legally intertwined with each other.
The bonus it gives to smaller states (which have more senate seats and electoral votes per capita) is rarely outcome determinative, and doesn't influence campaigning much because in the electoral college, the pertinent factor for a campaign is not which states have the highest electoral votes to voter ratios. Instead, what matters to a campaign are the states where voters are most evenly divided. States that strongly favor one candidate or another are usually treated like lost causes.
Historically, the electoral college was also important because the percentage of the population that was allowed to vote varied a great deal from state to state. This made popular vote totals less than apples to apples comparisons between states. If one state limited the vote to property owners (a common requirement at the time of the founding and something that is still not clearly unconstitutional, even though no state uses this requirement), and another didn't, it had a big impact on the popular vote. Now, much of the difference in voter turnout comes from the relatively importance of a state's electoral votes in the national election, and there is an emerging consenus that almost every citizen who is at least eighteen years old should be allowed to vote.
We know from experience that now and then the electoral college does not give us the same winner of an election as the popular vote does in a close election. There is a good case to be made that its justice is too rough. But, the electoral college almost always reaches the same result as the popular vote (but by an exaggerated margin) in races that don't have a close popular vote, even though it theoretically doesn't have to work that way in practice.
An electoral college that awarded one electoral vote in each Congressional District would provide even better insulation against an uncertain electoral result in a close election, while at the same time more closely matching the popular vote.
The electoral college is, by design, closer to the popular vote than having Congress resolve a close election under the proceedures that apply when no one candidate receives a majority of the electoral college vote (where states Congressional delegates vote on a state by state basis). And, the electoral college also provides a decent way to resolve Presidential succession in the currently unprecedented case in which a President-Elect dies or is otherwise unable to serve after being nominated by that person's political party's National Convention and before the electoral college votes in December.
Indeed, one good alternative to the current constitutional rule for Presidential succcession if there were vacancies in both the Presidency and Vice Presidency would be to have the electors who voted for the winner (it is not a secret ballot) serve as the vacancy committee in that situation, thereby reducing the likelihood of a transfer of power to a member of Congress or cabinet member who had very different political views than the President or Vice President who was elected by voters.
As a footnote, another really interesting recent mathematical result pertinent to politics is that one procedural way to eliminante the partisan biases of gerrymandering in a two party system is to let one party draw districts for half of the population, while the other draws districts for the other half of the population, regardless of the political makeup of the respective jurisdictions. This suggests that the founders hit upon a fundamentally good approach when they entrusted Congressional district drawing to the states rather than to Congress, which tends to split partisan control of the process. At the state level, it suggests that one solution to gerrymandering would be to give one party the right to draw district lines for a state house, while the other draws district lines for a state senate, and to alternate each census.
The electoral college's virtue in assigning electoral votes at the at large state level for the most part, over assigning electoral votes to Congressional Districts, is that it largely eliminates from the election system any opportunity to gerrymander in the Presidential election by those currently in power at any level. It also prevents the single member district system of electing members to Congress from acquiring constitutional status, leaving open the door to approaches to electing members of Congress such as proportional representation that would make politically possible a more than two party system.
On the other hand, the electoral college gives undue important to third party candidates with no real chance of winning.