Is the Republican party left or right?

The easy way to remember this is the three "R"'s - Republican-Right-Red, from which then you can deduce that Democrats are blue.

The red and blue thing came from a news network map during one of the elections when they were showing which states voted which way. Red and blue make a good contrast on color TV.

Blue, particularly dark blue, is often associated with Conservative parties, originating from its use by that party of the United Kingdom.

Red is traditionally associated with socialism and communism.

Thus says wikipedia.

In the United States, since the year 2000, the mass media has begun to associate red with the Republican Party, but the party has not adopted red in any official sense. I personally speculate that the association of red with the Republican party stems from the Democratic party's desire to distance themselves from the association with Socialism and Communism. But that's a conclusion you'll have to make for yourself.