In January of 1947 a patent was filed in the United States by Thomas T. Goldsmith Jr. and Estle Ray Mann for an interactive electronic game called the Cathode Ray Tube Amusement Device. It used analog circuitry to display a missile game on a cathode ray tube (basically an early television screen). Basically this was a simple missile simulation game in which a player could move a dot on a screen. The Cathode Ray Tube Amusement Device was a gigantic, bulky early computer hooked up to a cathode ray tube. The patent was eventually approved in December of 1948.
Does this qualify as the very first video game? Some historians suggest it does, and I tend to agree with them, but others argue the Cathode Ray Tube Amusement Device is only a precursor to video games and not a true video game because it did not utilize raster (bitmap) graphics nor did it use a digital display. Personally I think this is skipping the point since the term "video game" has become a semi-generic term to mean many different types of electronic games that make use of a viewing screen.
But to go further a few years, in 1952 University of Cambridge Professor Alexander S. Douglas created the first game to use a digital display. The game was known as Naughts and Crosses, and is basically the game to tic-tac-toe.
Then in 1958 the game Tennis for Two was created by physicist William Higinbotham for the Brookhaven National Laboratory. Used was an analog computer with an oscilloscope as the display device utilizing vector graphics.
Then in 1961 along comes Spacewar! It even sounds like a video game, doesn't it? Two MIT students, Wayne Wiitanen and Steve Russell are credited with making this game with vector display graphics.
So far, none of these games mentioned were ever released to the general public.
Now we got to the first home gaming system for sale to the public. It was originally known as the Brown Box, but when it hit the stores in 1972 it was officially called the Odyssey, made by Magnavox. The Odyssey, created by Ralph Baer who had been working on the project off and on for nearly 20 years, could be hooked up directly to a television. The earlier prototype, the Brown Box, then is the first video game system to use raster graphics.
So, does the Brown Box or the Odyssey qualify as the first video game? Opinions will vary, of course, and you can make your own decision, but I'll stick with the Cathode Ray Tube Amusement Device from way back in 1947.