This is not necessarily an awesome cheat, but it is something that I happened to stumble upon while playing. Thus far, this code has worked for Gradius II so I imagine that it will work for all of the games.

Basically, get a few power-ups, and then save your game. After saving, load your game and you will notice that the power-ups that you earned are still there. So, if you keep doing this, you will eventually have a full arsenal.