Have You Played? is an endless stream of game recommendations. One a day, every day of the year, perhaps for all time.
And yes, I'm calling it that, because as wonderful as the modern version is, 'The Ur-Quan Masters' [official site] is the worst name imaginable this side of Poopy McPoop's Wacky Space Hijinx.
I love being given a ship and a universe of stories to explore. Star Control 2 offers one of the best. You're a captain aboard humanity's most powerful ship, returning to Earth to find it encased in a forcefield by a powerful alien race. This of course Will Not Stand. Luckily, you're carrying a hold full of lost technology and there's no shortage of potential allies, if you can persuade them to join, in a galaxy sprawling epic known for its ridiculous scope, its character, and best of all, its snark. "What shall we name our alliance?" asks your one ally at the start. "The Empire of MEEEEEEEE!" you can reply, pulling a space-wheelie around Uranus. That sound you hear is Mass Effect taking notes.
The actual game is a mix of RPG and a funky combat system that's a bit like the old Spacewar, only with a whole fleet of different ships. There's a Super Melee mode where you can just go up against another player with whatever you want, and that's awesome, but in the main game you can only fight with what you've managed to acquire. The Mycon Podship for instance, slow but with homing missiles. The Ur-Quan Dreadnaught, launching fighters. The Syreen Penetrator, which looks like... ahem. The Spathi Eluder, which due to being piloted by cowards, only shoots from the rear.
It's such a pleasure to meet and deal with all these races, with that same sense of turning the tables on an unstoppable enemy as the likes of XCOM. It's also pretty free-form, albeit with some mandatory elements, giving a real feeling of fighting a guerilla war and stocking up with everything you need to survive. It was a classic at the time, and its modern version is still great.
Just... ah... don't ask about Star Control 3. It never happened. Never. Happened.