[Edit: I realise a lot of this has been discussed already, but its sort of one big idea ball and it does have a few not-so-common takes on things.]

So far I'm really loving the game, but I'd love to see a few things added to fill out some areas.

First is mining asteroids. Right now you scan, mine, sell, repeat. I'd like to see a little more fluff and a little more depth added to this procedure.
For starters, I like spinning asteroids but I'd love it if I could use my flight computer to automatically sync up with them. If I could do that I'd love to see them all moving/spinning to different degrees (to make combat a lot more interesting in asteroid fields).
I'd also like to be able to install beacons and devices on individual asteroids. A little pulse beacon I can deploy from my cargo bay onto a targeted asteroid would be nice. I set the frequency, tune my ship into it, and it will show up on my radar as yellow instead of gray and have a note on its info sheet when targeted. Depending on the model you purchase it will last 30 minutes, an hour or two hours. The highest end model could even record and transmit the content after it has been scanned.
Another item that would be nice is a coolant bomb. Again, you deploy it from the cargo bay onto a targeted asteroid. Over a short period of time it will lower the temperature by 20k, 30k or even 40k depending on the model.
A tether item would also be quite handy (not just for mining, but also hiding). It essentially ties you down to the asteroid at say, 10m, and locks you in position. Mining this close causes the heat to rise faster but it also prevents you from showing up on certain scans and quick-find (x button) targeting. This allows you to mine the more expensive, higher risk materials. Sacrificing speed and efficiency for safety.

This tether idea brings me to the other area, anti-combat. When a pirate shows up you can either pay, flee or fight. The only option there with any depth is fight (and the pirate usually has the advantage). Rather than complaining that its unfair I'd like to suggest the ability to fight back with dirty tricks.
If a pirate wants 50,000 credits and I just happen to have a stock of 50,000 (fake) credits in my cargo bay, maybe I'll be able to get enough of a head start to get away while he verifies that they're real.
Another dirty trick would be an EMP bomb. Stored in the cargo bay, you set it off and it will disable all weapon systems within a certain radius for 10-20 seconds. On the higher end models it also disables the engines of any ship that doesn't have its protective shield set to the right frequency (or something like that, just a way of making it so you can give your group a number to type in so they can escape with you).
I mentioned the tether earlier. This would be great for when a pirate ship drops into the sector and you need time to call in backup or wait for them to pass by. It would also be good for pirates to help them camp out, although for this reason I'd suggest making it so that your own scanners are weakened while tethered (otherwise it might be a bit too good for camping).
Something that hides/scrambles your jump co-ordinates would be great too.

These are just some rough ideas, but the basic concept is simple. I want to be able to trade off cargo bay slots for ways to help protect against the various threats out there. If I have to reduce the amount of cargo I'm carrying in order to increase my chances of delivering it in one piece that's a payoff I'm willing got make.
Naturally I don't want to eliminate the threat of piracy. If this stuff works too well then piracy will turn into mindless player-killing. I just think in a world where piracy and player killing is an option you need enough clever tricks that you can balance it out into duel of wits.