There is a company called "37signals"

According to Wikipedia: "The company 37signals was originally named after the 37 extraterrestrial radio signals identified by astronomer Paul Horowitz as potential messages from extraterrestrial intelligence."

There are 37 holes in the mouthpiece of a telephone

I'm talking about "old" style phones with the "Mickey Mouse" handsets that have the round mouthpieces

There are 37 bars in the digits of a digital watch

It has to be a 12-hour-mode display, and you have to count the seconds

In a "3-4-5" right triangle, the small angle is approximately 37 degrees

And so the sine, cosine, and tangent of 37 degrees are approximately 3/5, 4/5, and 3/4, respectively. This in turn means you can do easy calculations with these trigonometric values without needing a calculator. Because of all this, 37 degrees is a popular angle for use in physics tests.

The 37th Amendment guarantees that you can post whatever the hell you want to the net

From the Flamers' Bible, by Joe Talmadge, written in 1987, posted to rec.humor.funny Way Back When, and reappearing in rec.humor.funny.reruns in August 1997.