I'll give you the Alaska perspective, and hopefully someone else can chime in with the rest of the story. In short, the invention of the telegraph is the technological turning point. Before the telegraph, American presidential elections could take weeks. University of Alaska professor Terrence Cole has a particularly good example of this. He'll throw up a Nome newspaper that announces the results of the 1900 presidential election in a huge bold headline befitting a breaking story ... that newspaper is from January 1901. Four years later, after Nome is connected to the telegraph, the results of the U.S. presidential election arrive in Nome the same day and are in the newspaper the morning after election day. Just think: 110 years ago, the results of the U.S. presidential election could be transmitted around the world on the day of the event.

Now, I don't have the Nome newspapers handy, unfortunately. What I do have handy are newspapers from 1912 that illustrate the importance of the election. Check out the Election Day evening newspaper Alaska Daily Empire from Nov. 5, 1912. (Click on the gear at the upper right hand corner of the image and select full resolution if it's too small to read.) You're already seeing lead election results from the East Coast of the United States on the day of the election.

Now look at the next day's newspaper. You've got full results from the U.S. presidential election, in Alaska, on the day after. Now, Alaskans couldn't vote in presidential elections until 1960, but 1912 was the first year they could vote for delegates to the territorial legislature, Alaska having become a U.S. territory in August 1912. Here, you see the true power of the telegraph. You have results from across the vast and unsettled territory, from Fairbanks to Cordova and Seward. Everywhere the telegraph touches, you have information.

Look down at the bottom right-hand corner, and you'll see what happens when there is no telegraph. The telegraph lines from Valdez and Ketchikan and Wrangell and Petersburg are down, so there are no returns.

What about farther back? Well, 1912 was the first year Alaska had elections, so I'll have to refer to my good friend the New York Times. Let's see what the Times had to say on Nov. 7, 1860, the day after Lincoln's election. Golly, would you look at that! Results from across New York and the Northeast -- and not just presidential results, state results, too.

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I do have one quibble with your question, and it's this: Even today, elections don't wrap up in a single day. Take a look at this calendar from the Alaska Division of Elections to see what I mean. Nov. 4 may be the general election day, but the deadline for receiving mailed-in ballots isn't until Nov. 19 if they're sent from overseas addresses. Absentee and challenged ballots will be counted up until then. Depending on the closeness of the race, the result could change even after Election Day. It's important to remember that although we think of Election Day, plenty of work goes on afterward, too.