Star Control (1) (1990, Accolade) centered around arcade-style spaceship combat, but included a strategic "campaign game" where opposing sides explored a small galaxy and could build mines, colonies, etc.
Star Control III (1996, Accolade) was not good. In addition to the arcade combat, it had a cheesy adventure game with bad dialogue and many bad design elements. The combat wasn't as bad as the adventure game, but had some balance issues. -MikeBuchanan
Star Control II (1992, Accolade) was the best. Like its precursor, it has arcade-style spaceship combat, now augmented by a 4xish system of exploration, resource harvesting, and ship upgrading, all contained within an epic adventure game. Your character was born on a splinter colony of humans resulting from a failed mission. On that planet, ancient technology from a mysterious race known as the Precursors was discovered and coaxed into building a flagship. You have a rapport with the technology and so are chosen as the pilot. Upon returning to Earth, you find it enclosed in a slave shield by the evil Ur-Quan, with an orbiting starbase your only contact. You take it upon yourself to find allies against the Ur-Quan and free the races they have enslaved. Your task takes you all over a star quadrant, exploring, mining, fighting, and negotiating. -MikeBuchanan