These are all good options but would also like to suggest something different..........Space Rangers 2
Great game. I really got into the universe when I got imprisoned on a planet where I wasn't welcome, and broke out through an old-school style 'choose your own adventure' styled story. Really cool to see that integrated into a game.
Also, if you can stomach the old graphics, check out Wing Commander: Privateer. It's an open game. Only 4 ships (your starter one, a 'trader' type ship, a 'tank' type ship, and a high-end combat ship) but I've lost many
hours months on it. If the graphics are too poor for you, look into the Vegastrike Privateer mods. The Gemini Gold and Privateer Universe ones are both great - Gemini Gold holds true to the original (basically a near-replica with updated graphics) and Privateer Universe greatly expands - allowing you to pilot nearly every other ship in the game, new weapons, etc.
Edit: Sorry, missed the open world. But I can still suggest FS2 if you like space games at all, it's fantastic. Tons of user-made missions along with the wonderful campaign
Also, I can suggest FS2... can grab it on GoG and then grab the FS2 SCP - it's an update that brings the graphics VERY close to modern day graphics. GREAT storyline (IMO), great gameplay. With the SCP, it's about on par (give or take) with newer space games. Can't recommend this one enough if you want an old school Wing Commander/X-Wing/TIE Fighter styled game with a smoother and more modern feel.
Link to the FS2 SCP install guide on GoG:
http://www.gog.com/en/forum/freespace_series/quick_and_simple_freespace_2_scp_installation_guide/page1If you still need convincing, check this out -
http://www.youtube.com/watch?v=8HFEmGcJcWA - jump to ~1:20 for gameplay footage.