3030 Deathwar check the download section http://spacesimcentral.com/ssc/files/file/364-3030-deathwar/ for the free version or you can pay a couple of quid for a updated version here http://crunchyleafgames.itch.io/3030-deathwar and well worth it as it one of the best 2D elite clones around.

And it's also available on Desura as well.

Does "Space, Pirates and Zombies" count? Can't really think of many games in this style. I'd like to know of others personally. The Last Federation is also a pretty good game. It has really unique gamwplay

Might want to check out "VoidExpanse", now on Steam.  It is sort of a combination of an Elite-type trading game with a Diablo-like action RPG, except that it features 2D Newtonian physics.  To me, the most attractive feature of it is that you can fit your ship with all sorts of interesting tech that drops as loot.  They never got the controls quite right, and they could really use a much bigger variety of items of each type, but it's still good fun.

In the same vein, you might want to check out "Drox Operative" also available on Steam.  It's a little light on the trading aspects, and it's more an action RPG, but it's brilliant.  It has two amazing innovations: it is an action RPG set inside a 4X game being played out by AI's, and ship modules (which drop as loot) can be fitted into generic slots (like in EVE).  It is one of the drabbest looking games ever made, and it's a little lacking in content, but it's something special.

Should check out Naev another free one http://blog.naev.org/ long time since I played it but a few have recommended it in the past.also theirs Ring Runners:flight of the sages http://ringrunner.net/ not to every one taste but I think you can download a demo of it.

http://www.cornutopia.co.uk/lif/

might wanna check out this one. Uses 3d graphics in a top down view. Its a quite old game, but the developer is really polite and frequently updates his games for new OS's.

http://www.anarkisgaming.com/unending-galaxy-info/

This one is a bit out of the scope of your question, but may be very interesting too.

http://desura.com/games/oresome

this one isn't being developed any further, but is nonetheless an interesting game.

Space ranger can be fun but you do tend to die a lot in it, can be bought on Steam, GoG ect and theirs the Escape Velocity series http://www.ambrosiasw.com/games/ev/ mostly Mac game but some of them have PC versions as well.

My game!  http://www.evglabs.com/starshipcommand

Although, as of right now it is a little more on the combat side. But you could "win" the game economically also.

I've registered with SSC just to respond to your query!

My favorite top down 2d space sim is without doubt Transcendence.

http://neurohack.com/transcendence/index.html

It plays like a rougelike with each level/system randomly generated but with some important systems always present.

Huge variety of weapons, armour and equipment.

The best part is that the base game is free. There are a couple of paid expansions, but I have put many hours into playing just the original game.

Another game you may want to look into is Starsector.

http://fractalsoftworks.com/

I have to admit that I havn't played it yet as it is still in development, but I have followed its development progress on their website for the past few months and it looks promising.

Hope this has been of some help.

Prospector http://www.prospector.at/forum/about.php a great rogue-like with ship and ground combat, planetary exploration and survey missions, recovery of alien ships and lots more. I recommend it if you are at all into old school rogue-likes (with the tons of keys and ever ongoing development and basic graphics) and its completely free.

Destination Sol http://store.steampowered.com/app/342980 is open source and free on steam but pretty basic right now. don't think it has any quests just explore the galaxy and fight to get money/upgrades but may develop into something great. These guys are the new Devs who took over recently http://forum.terasology.org/forum/destination-sol.57/ .

Wow there were 3 games in this thread I hadn't heard of (Oresome, Unending Galaxy and eglabs Starship Commander) and I see that 2 great freeware space games have had updates since I last checked them out, (Transcendence and NAEV, which I thought was dead) so thanks guys.

This is self-promotion, but if you're interested in space trading and combat games (similar to the previously mentioned Escape Velocity and NAEV), you might take a look at Endless Sky:

http://endless-sky.github.io/

It's a 2D top-down game where you can earn a living through anything from carrying cargo and passengers, to fighting pirates, to taking sides in a civil war. We're in final beta stages right now, and it seems like each beta tester comes up with a completely different style of play: anything from building a massive merchant fleet to poaching alien ships and stealing their technology. Also, it's open source, and is designed to make it (relatively) easy to add your own content.

Whats this I see before me? A thread about 2D space sims and no mention of the mighty Star Control games!?!

Ok I will fix that.

These games are gettin on a bit now but there are still awesome, check out the Wiki about em <here>, also rumours of a remake <here>. As for the games themselves you can pick em up on GOG for very little. Or you could go for a fan created remake called Ur-Quan Masters <here> which is free and based on Star Control 2.

Lets not forget Star Flight 1&2 as well as Space Rogue the old Origin game not the new FLT like one.

I would also recommend starsonata which is an amazing mmo within this genre.

The Escape Velocity series is an absolute classic, and deserves more than a sidelong mention.

There is a new version of 3030 Deathwar coming out on Steam Early Access!

Here's the link: 3030 Deathwar Redux on Steam

U have to play in Space Rangers.