I don’t see a list module ideas yet, so here we go! I haven’t finished single player by far, so have yet to see the special race-specific modules (I hear there’s a lightning gun out there…), but here’s some ideas to start things off:
Really Big Powerful Beam: Mentioned before I’m sure, the classic giant energy beam, maybe even with a slow charge, fires for continously for a couple seconds and does ridiculous damage (maybe even to multiple ships), and a super long recharge. Idea for the large weapons in general - maybe have a class of weapons where entire ship has to move to aim it/only fires forwards (maybe a “big” version of most weapons). Making it take up lots of space can be done by having it require gobs of power - more than can be supplied by a single power generator (or even two!)
Teleport Self: Short range teleport (maybe an animation like the Battlestar Galactica jump?). Good for getting moving those into position/turning quickly for those big cruisers. Long cooldown. Fighers especially could use this.
Teleport Ally: This should be expensive/require lots of power but similarly, can let you pull forward some of those slow ships.
Linked/Networked gun: kinda the reverse of chain lightning, a gun that’s more powerful if there are more of guns of the same type nearby. Could follow a chain that could span your entire fleet (but probably some kind of diminishing returns)
Ramming Shield: Very short range weapon that converts your shield into damage.
Suicide Bomb: Does (area) damage when ship is destroyed. If area damage, should also affect allies.
Missile Array: Fires a large number of missiles, then slowly reloads. For the truly gratuitously overpowered alpha strike 
Afterburner: for fighters (since they need more variety) - short burst of high speed, long reload.