Rapid-fire is lethal. It pretty much guarantee's your ship to attack twice, if not three times in a single round provided that it has targeted an enemy ship or defence which it has rapid fire against.
It is the 'hard-counter' in oGame. And since you don't care about SC2 I'll elaborate. Combat takes up to 6 rounds, and within each round, each attacking ship will select a random defending ship or defence and shoot at it. If the attacking ship has rapid fire against the target it chose, there is a further chance (determined by the Rapid fire rating) that the ship will fire again, but this time picking a new target. So, if the enemy fleet consists of one ship-type, the attacking fleet will have crazy rapid-fire and most likely come out on top. As soon as the attacking ship picks a target against which it has no rapid fire - it ends its round there.
Ships and defences are not removed from combat DURING the round, however. So it is possible for a ship to qualify for rapid-fire, then retarget, but actually target a ship or defence which has already been destroyed - effectively wasting the shot. This was actually a bug in the early oGame days, but it has become a part of game-play as the major catch which stops Rapid Fire becoming too powerful.
So, to counter rapid-fire, you put fodder in your fleet compositions. Instead of attacking someone with 20 cruisers, you would attack him with 20 cruisers and 50 light fighters. Or, another example, you don't build a fleet 100% out of Battleships because Battlecruisers kill them at a 2:1 ratio - due to rapid fire. Knowing which ships have rapid fire against which other ships, is the real strategy in oGame other than simply being active and paying attention (espionage/rankings).
In short:
Cruisers kill Light Fighters
Heavy Fighters kill Cruisers
Battle Cruisers kill Battleships and Heavy Fighters
Destroyers kill Battle Cruisers
And since ships target each other randomly, a fleet consisting of 90% Light Fighters and 10% Destroyers, will effectively mean that the Light Fighters will take 90% of the incoming damage. Which is a good thing when none of your opponents ships have Rapid Fire against Light-Fighters, but a bad thing if the opposite is true.
None.