The absolute first video game I remember playing was Pong, like many older people. In the arcade I remember Tempest being my favorite, not sure if it was the first though. I don't really count those because they weren't PC games.
My first real PC Game I remember playing was Ultima III in high school. A friend had a cracked copy and we would ditch out of class and go to the Social Studies lab and play it on their glorious Apple IIe PCs in beautiful CRT Green (haha). When we beat the game we used a hex editor to restructure the map and make a bunch of custom mob changes and then played through it again.