Well, there is

Freelancer - Very good game, nice open galaxy plus quite a few mods that add loads of detail.

X2: The Threat - Sorta like freelancer. Geared more towards combat.

X3: Reunion - Like X2 but updated. Lots of stuff to do and try and some pretty cool mods as well.

Those are the three main ones I can think of now. Those would probably be most closely related to EVE.

I would higly...HIGHLY suggest X3 Reunion.

Not only does it look and play amazingly...but tons of support, mods, scripts, and still after all these years an active community. So many mods that it adds hours to the game...seriously. One of the BEST stories ever as well. There is also in the 2nd or 3rd quarter a new X3 game coming out.

And finally...it is the most like EVE but offline.

One warning. Dont expect to just jump into it. Its a large game and takes time to grasp. By large I mean the map is HUGE, the ship types are HUGE, the trading is HUGE, the combat is HUGE. So much to do its mind blowing. I say give it a full 2-4 weeks of playtime to really understand all the different stuff...but then again thats what makes it fun.