I've played WWII submarine video games sporadically through my life. And whether it be "Silent Service" on my Atari 800, or "Pacific Fleet" on my iPad, one question has always stuck with me - how were submarines able to launch a torpedo on any azimuth other than the exact direction the sub was facing? In these games, and in movies, etc. the player/captain spins the periscope, aligns with the target (leading it if necessary) and fires a torpedo. How can the torpedo go in any direction other than perfectly straight? With a shipboard gun, a turret could spin to deflect from the course of the firing vessel. Torpedo tubes presumably didn't spin, and were fixed in place like a rifle barrel. Was there a rudder pre-set on torpedoes? In which case, wouldn't its course be an arc versus the straight line presented in video games?
Torpedoes had gyroscopic guidance systems. Given the target's range, speed, and heading, the firing control computers or weapons officers would calculate a "gyro angle" for the torpedo. The gyroscopic guidance on the torpedo was set to this angle before launch, and after firing would use the rudders on the torpedo to turn it onto that desired angle and then maintain it. A pressure sensor and dive-planes were used to keep a desired depth in a similar fashion. Different torpedo types had different gyro angle limits, but I don't know these off the top of my head. While torpedoes could be made to turn as far as this gyro angle after launch, it was recommended to fire at the smallest gyro angle possible to avoid the potential for error in what was a complicated mechanical system. As the gyro angles increased, the chance of the torpedo settling on the wrong course increased as well. Also, there was the potential for something known as a "circle runner", where the torpedo's rudder was jammed during the turn and did not straightened out. The American submarine USS Tang, commanded by the US's top submarine ace, Richard O'Kane, was hit and sunk by one of it's own torpedoes in this way.
Later in the war, even more advanced torpedo guidance systems began to appear. The German FAT system allowed torpedoes to be set to turn 90 degrees left or right after going a certain distance, and then alternating this in a ladder pattern to increase the chances of a hit if the initial shot missed. The subsequent LUT system allowed this initial turn to be any angle, rather than just 90, so that the ladder pattern didn't need to be initialized at a right angle from the target. Also, both the Germans and Americans developed acoustic homing torpedoes, which would turn to maximize signal strength from a hydrophone. All of the above applies monstly to the German and American submarine forces, I don't know as much about the technical side of the British, Italians, Soviets, and Japanese, but I would imagine that their torpedoes had gyro angle settings at the least, especially considering the excellence of Japanese torpedo design.
This website is a great resource for the German submarine arm, and the page linked goes into basic detail about different torpedo types. O'Kane and Fluckey's memoirs give good insight from the American perspective.