I'm going to answer this as a political scientist and hope that a historian will chime in to provide historical background on the evolution of the party system in the USA, as my knowledge of the area is murky at best.

But from a PolSci viewpoint, the USA have a two-party system, quite simply, as a result of their electoral system. The US famously votes, same as for example the UK, in a system dubbed "first past the post" or "the winner takes it all". In this system, as everyone knows, the candidate with the relative most votes in a certain voting district wins, no matter the actual percentage of votes he accumulated. He can win if he's got 2%, as long as there are 98 other candidates running who all only got a 1% share of the votes.

Now, voters are, contrary to the hilarious quips of saturday night comedians, not stupid. They know their votes will be wasted if they vote for a candidate that has no hope of winning. So they pick a promising candidate that is the least far away from their political standpoint and vote for him. But inherently, this means the political system will gravitate towards a two-party system, as all the smaller parties gradually succumb to the fact that they will never have a chance to win anything because they would need to instantly accumulate a huge percentage of votes.

Statistically speaking, "first past the post" voting systems evolve into or towards a two-party system. The US is a very extreme example, as there are really no other parties represented at all, but even the UK, which has some smaller parties represented in the House of Commons, is undoubtedly a two-party system with only two major parties alternating in ruling (although they do have had some periods when a coalition was needed, something that is commonly attributed to the strong political fracturing of the UK as an entity, with many local political scenes).

/u/Kartoffelplotz gave a good run down of why the first-past-the-post system tends to lead to a two party system (there have been exceptions, in the US, and even stronger ones in Canadian and UK political history. The UK is even sometimes called a 2.5 party system). I'll get into the other part if your question a bit.

In American history, there are many examples of presidential victors that've won with less than 50% of the vote. The infamous 1824 election led to a four-way split and the formal development of the Whig and Democratic parties. The 1860 election led to a split that led to the development of a new party system after the Civil War. Populist parties popped up in the late 19th century and shaved some percentage points from the victors (though not electoral votes, unless I'm mistaken). 1912, Teddy Roosevelt started a new party and actually outdid the Republican candidate, leading to Woodrow Wilson's victory. 1968 had George Wallace run a fairly strong 3rd party campaign. 1980 had a libertarian candidate get 6% of the vote, but didn't stop Reagan from breaking 50%. 1992 had Clinton win with 43%, since Ross Perot ran a strong campaign. And to break the 20 year rule, the 1996 and 2000 elections had the victor win with less than a majority.