As much as I like this particular niche, I've only played a few of the games listed. If something is missing, or one I've added doesn't belong - which is likely - please let me know!
What is here? Like the title says, games where the player controls a spaceship in real time on a 2D plane (and hopefully has an adventure!). No 3D movement, no turn-based space movement, and at least some attempt at plot or role-playing-ness - i.e. no shmups, and probably few twin-stick shooters and multiplayer games.
Suitable games in active development: Sol Trader, Wayward Terran Frontier: Zero Falls, Epiar, Sol Ark, Exo Miner,
Abandoned games: Final Frontier Trader (2004), Epoch Star (2006), Darkverse (2011?), Abraxium (2011), Project 6014 (2012), sgii (2013), Stars of Icarus (2014)
Almost-suitable games: Star Nomad Elite (not on PC), Starport: Galactic Empires (MMO), Star Sonata (MMO), Scum of the Universe (arcadey), Fusion: Genesis (not on PC, mostly multiplayer twin-stick shooter)
I had a hope that making this list would help me find a game I barely remember from perhaps a decade ago. While it hasn't turned up yet, I've found maybe half a dozen more that do belong, so time spent looking hasn't been wasted.
Update, many years after I originally made this (probably with a bunch of new games now deserving to be on here): the game I wanted to find was Starfight VI: Gatekeepers.
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The quick look of this reminded me how much I enjoy these games, and is responsible for the list existing, but I've not actually played it.
Only just worthy of inclusion, but I shouldn't be too harsh on a game from 1992.
I don't know how I feel about putting this one on the list - movement is 2D, but it's not top-down. The sequel, of course, has no chance.
