We've written about Starsector [official site] before. It went by a different name then, starfarer, but it's the same densely packed space RPG today as it was back then. More so, in fact, thanks to the recent release of version 0.7a, which added new ships, weapons, system-specific abilities, sensor mechanics, space terrain and recruitable combat officers, along with even bigger battles. I haven't played for a couple of years but found the focus on singleplayer and ability to command fleets very compelling. I'm keen to see more.
Starsector is an Elite-like. A game in which spaceships are your avatar as you seek fame and fortune in an open world, that allows for trading, piracy, inter-faction military actions and exploitation of surrounding systems (and that's both game systems and star systems). You can buy it now, for instant access to the alpha version and all new releases. It's compatible with Windows, Mac and Linux.
The first time I played I was surprised by how flagship-centric the action is, having expected a fleet management game rather than a space-based RPG. While it is possible to add ships to your fleet, and to give them instructions when you enter combat, there's also fun to be had exploring the procedurally-generated galactic sectors.
Development seems to have been coming along well in the years since that first look. The "bigger battles" mentioned above are a more significant addition than you might imagine: rather than simply ramping up the number of ships allowed in combat, there's a new system in place that allows nearby fleets to join ongoing fights, making the galaxy even more dynamic. Even more alive.