A new galaxy every time you play, offhand I think Space Ranger 2 does this but it more 2D, Rebel Galaxy and Astrox maybe as well.

Pretty sure their are a few which do this but I think they are more likely to be 2D games than 3d ones.

Oh Pulsar does this apart from the start location or maybe it the ship you start on.

Oolite can be adapted to do that, I think (even if only changing the seed manually).

1. Flatspace and Flatspace 2, comes to mind too. 2D though.

2. Everspace is coming soon, randomly generated each time, but it's more rogue-like action-packed space game with top notch graphics. I've played an alpha version before and I can say it's really cool.

3. There's also Evochron series, although they're not randomly generated, but still worth to check it out.

4. Sol Trader.

The game combines 2D Elite style gameplay with a random generated society you can really get to know. The game revolves around getting to know these characters and doing missions for them.

5. 3030 Deathwar (Redux)

3030 Deathwar is an Open World 2D Space RPG. Similar to games like Escape Velocity Nova and Elite/Privateer, the game features Open World exploration, boarding stations and derelicts, many diverse NPCs, tons of missions and an exciting plot! The new version adds higher resolution, massive balance and gameplay changes, a smoother tutorial and many other improvements!

6. Drox Operative

Drox Operative is a starship action RPG with warring alien races, fierce space battles, a dynamic, evolving galaxy, and co-op multiplayer for Windows, Mac, and Linux.

7. Transcendence

In Transcendence you are thrust into the middle of a vast galaxy teeming with clashing empires, expansionist AIs, and fearsome xenophobes. You must navigate them all to reach the Galactic Core. Adapt your strategy to survive the journey through dozens of randomly generated star systems. Take advantage of scavenged weapons and devices. No two games are ever alike, so adaptation equals survival.

8. SPAZ 1 and 2

P.S.

Some games might not fit your bill, but I'm posting them anyway just in case you'll decide to try them out.

Infinite Space Sea of Stars http://store.steampowered.com/app/269990/

Empyrion is such a game, the systems are randomly generated based on a set 8/9 number seed, same number = same universe, different number = different universe.

Empyrion is a mix of FPS, building, survival based on space travel and exploration. The game has different starting modes as for locations that can be totally random and where you must survive by gathering and crafting objects, build buildings and spaceships etc. The game starts by droping your ejection capsule onto a planet or moon after which you are on your own. Or: you can chose to start on a life-friendly planet to get you an easier start.

It is a Minecraft game but with much better grafics and also: very demanding as for system requirements.

The game comes with a comprehensive inside tutorial and knowledgebase that you can pop-up at any time if need be, very handsome.

Although the game is in development and alpha state, it has the most content playable that I have ever seen in a pre-release game. Playable means: the features actually work without frequent crashing. There is a lot to do, build, fight and explore.

I haven't tryed it out for longer (high system requirements!), but I will for sure, the price is very reasonable, around 20$ I think.

http://store.steampowered.com/app/383120

http://empyriongame.com/

Greets,

XenonS