Some has mentioned "Pirates". I actually think "Sea Dogs" (PC game) has redefined that genre. If you were into the original Pirates, you MUST try Sea Dogs.
Anyway, other titles to remember:
Space Crusade... Though I haven´t really seen that many games in that genre. It still rocks though ;-)
Cabal is also a real classic, but like Space Crusade, there really hasn´t been many games in the genre.
Someone mentioned "Double Dragon". I actually think "Golden Axe" was the first in this whole genre... Remember, Sega launched the game as an arcade game long before it was ported to the Amiga.
Apart from that, the following titles deserves at least an honorable mention:
Moonstone
Nitro
Lotus 2
Ports of Call
Pinball Dreams
Sword of Sodan
Wings of Fury (perhaps)
