According to E. Nelson Bridwell, in the introduction to Superman: From the Thirties through the Seventies, the costume was designed to look like that of a circus aerialist.
The red underwear was probably meant to break up the blue, which may have been too much for printing in the 1930s, especially with Superman's hair having blue highlights (or else it would just have been a blob of black ink). The cape was used to give the static drawings a sense of motion. It was waving, which meant that Superman was leaping. (The flying was added at the suggestion of the Fleisher studio.)
As far as updating the costume goes, it was updated in the comics a few years back, and then changed back to the classic. If you were to examine covers from all the decades, you would see a good deal of updating, with the S symbol growing or shrinking, and the color on the back changing. (George Reeves' cape had a full color insignia; in the comic, the insignia on the cape is all yellow.)
Why not update it further? Probably because it would offend the fan base, the people who would go see the film the first weekend automatically. The minor changes that Obi-Wan Pinobi mentioned caused a HUGE amount of controversy among the comic fans on the web. The X-Men, being less known by the general public, could have their costumes updated. Spider-man couldn't.
Oh, by the way, the quote "Truth, Justice and the American Way" does not come from the comic book. It started on the radio, where it was just "truth and justice." "The American Way" was added for the TV show, which was produced during the McCarthy era. It has always made little sense that Superman, who protects the entire world, would fight for the American way, since he would have to conquer all dictators, etc. This was recognized by the 1960s, and the cartoon show that came on about 1967 changed it to "truth, justice and freedom." Therefore, "truth, justice and that other stuff" is really very accurate.
