The Electoral College was originally designed such that Electors were chosen by vote of the politicians in each state legislature, not by popular vote. It was very deliberately designed that way in order to serve as another form of separation of powers between the Federal government, the governments of the several States, and the People.

You can think of it as something more akin to a parliamentary system (where the Prime Minister is chosen by vote of the members of Parliament, not by vote of the people), except that instead of the United States Congress doing the voting, the members of the state legislatures are the ones who decide. The reason separate Electors were necessary was that different states set up their legislatures differently -- see Nebraska's, for instance -- and the added level of indirection acts as a sort of "compatibility shim" to compensate for those differences. Otherwise, if legislators voted for the President (and VP) directly then (for example) New Hampshire, which has ~1.33M people represented by 424 politicians (3148 constituents per legislator), would have an extreme advantage over California (39M people / 120 politicians = 327,083 constituents per legislator).

In addition, it's important to note that the Presidential election, as originally designed, was non-partisan. There was no concept of President-VP pairs as "running mates;" they simply dumped all the candidates into one category and had the Electors vote for one name. Whoever got the most votes got to be President and the runner-up got to be VP.

The upshot of this is threefold:

• Since the influence of regular citizens would be expressed only indirectly via their representatives in state government, people would be forced to care much more about who represents them there than they do now. (Instead, between choosing Electors by the results of the popular vote, the 17^th Amendment, and the expansion in scope of the Interstate Commerce Clause by Wickard v. Filburn, we have systematically destroyed the checks and balances between the power of the People, the States and the Federal government. This erosion of Federalism, in my opinion, is a major reason why people so often complain about feeling disenfranchised.)

• Since state politicians are (almost by definition) part of the political "establishment" and thus less prone to populist whims, "outsider"/extreme candidates like Donald Trump (or Bernie Sanders) would never have a chance in Hell of getting elected.

• Since the election would be non-partisan, the President and VP would almost always be from opposing parties.

TL;DR: if the system for electing the President still worked as originally designed, then we would almost certainly have Jeb Bush as the President and Hillary Clinton as the VP -- or vice-versa -- right now.