How to play for free (and crash the game)
Like most arcade games, Galaga features an attract mode that shows you how the game is played. Before you insert a coin, the computer takes control of “your” ship to demonstrate how to shoot enemies, avoid enemy fire, get captured by the tractor beam, and retrieve your captured ship to double your fire power.
Interestingly, there is a bug in the game that lets you control the ship during certain portions of this demonstration. You get to effectively play the game for half a minute or so without spending any money.
Don Hodges has an excellent, detailed explanation of why this bug occurs, as well as some neat videos showing the bug in action.
As soon as the demo starts, you can use the fire button to shoot enemies. (The demo also fires on its own, regardless of player input.)
The key point in the demo is when the “boss” Galaga pauses to send down a tractor beam. If the demo runs normally, the ship is captured. However, you can cause the demo to veer off course by shooting the Galaga and disrupting the tractor beam before it captures the ship.
At that point you’ll be able to control the ship’s direction in addition to the fire button. Depending on the exact sequence of moves you make, and how long you take to make them, a number of different things may happen. The demo might let you continue shooting enemies until they’re all gone. It might end before you have a chance to finish (while possibly doing very weird things when you run into a tractor beam.)
And sometimes, it will just crash:
Despite the fact that this is a well-known bug, the creators declined to fix it when they re-released Galaga in the ’00s as half of the Ms. Pac-Man/Galaga - Class of 1981 arcade edition.
The only difference seems to be what happens after you crash it: on the Ms. Pac-Man/Galaga combo machines, a crash will be followed by a self-test that makes different Pac-Man sounds depending on whether you happen to be using the controls at the moment it crashes.
If you aren’t touching the controls, Pac-Man’s “extra lives” bell rings and the screen displays “OKAY” for each of the components checked.
If you are touching the controls (pressing the fire button or moving the joystick in any direction), the Pac-Man dying noise is played, and the screen displays “ERRORS EXIST” and “STUCK SWITCH” in red.
Once the self-test is done, the machine resumes its normal demo mode, and you can try the trick again.
Older Galaga machines have another exploit that you can use to cause the enemies to stop firing for the duration it takes to finish the game. StrategyWiki has details on how to do this; there's also a detailed code analysis here.
There’s also a Stage 256 bug, a common occurence with 8-bit arcade games (Pac-Man and Dig-Dug, among others, famously crash at the same level.) If you reach the 256th stage in Galaga, you may or may not be able to proceed, depending on how the machine’s difficulty level is set. Don Hodges offers a detailed explanation (and proposed fix) here.
One other well-known Galaga quirk is that there are only 6 digits reserved on the screen for the first player’s score, while there are 7 for the second player.