Alternate weapons are okay as long as the game can be balanced around them. You essentially are adding an additional balance point.

I assume most ships would have at least two weapons or abilities.  For example when I suggested the Gravitic Mine above I was thinking of it as the secondary system of a ship that had another "primary" weapon.  But this is Star Control, so I could see a ship with only one weapon.  A single weapon ship would probably be very fast and agile with a relatively weak weapon, or the opposite direction and be very slow and tough with a single powerful weapon.  But I imagine that most ships will probably have at least two weapons/devices.

Manually controlled missiles. When the player fires and keeps holding the fire button, he can make the missile turn left and right with his normal turning keys. The problem is, of course that he can't turn his own ship while doing this. Also, when the control is released (let go of the firing key) it can't be regained. The missile will keep flying straight, though it might be fun if it kept going in circles if you release control while turning.

Best suited for a sniper type ship.

Directional shield. Not impenetrable shield like Yehat shield, but a shield that stays up and absorbs something like 4 or 6 crew worth of damage before going down. It can be regenerated from full battery. It also only protects one quadrant of the ship and is turned with similar mechanism as Orz turret.