A long time ago I saw this video:
in which there's a space demo that used parallax, and I thought it looked amazing. Now I've finally found the resources to make my version of it, which turned out to be not too bad, and a lot more realistic than the cartoon-styled original.
You can check it out here: http://daem-on.ml/games/spacedemo/
As the text says, left click anywhere to show planets.
I know one of the planets is behind a layer of stars which is extremely unrealistic, but it looked really cool so I left it in.
I'm planning on writing a tutorial about this, so if you're interested in how I did it you could read that.