Television was (and is) an evolving technology and medium, so it's tough to pinpoint its specific birthdate. While some countries were ahead of the U.S. when it came to TV, the first stateside broadcast occurred in 1936. It was more of a test, especially considering there were only about three receivers in the country that could pick it up. You can watch that broadcast here. (If you love old men rambling in front of French doors, it's programming that has yet to be topped).
Three years later, on April 30, 1939, the first-ever regularly scheduled television broadcast began with scenes from the just-opened New York World's Fair. NBC beamed Franklin D. Roosevelt's World's Fair inaugural address from the antenna of the Empire State Building, and it reached tens upon tens of households. Here's a clip of what it looked like (just imagine you are watching on a five-inch, 441-line RCA electric television set):
RCA Advertisement, via Wikimedia Commons
Ten years later, NBC celebrated the anniversary with a program that included plenty of the footage shown during that first-ever scheduled broadcast. It's also a good example of how far the medium progressed in just a decade:
Happy Birthday, TV. Sorry this was on the Internet...you know how it is.