Thank you all for the replies, and yes a lot of the movies like Alien, The Thing, and various zombie movies.
Another idea I just thought up for the same type of scenario comes from an old, obscure comic called "Virus"
http://en.wikipedia.org/wiki/Virus_%28comic%29, SHODAN from System Shock, and the Re-Imagined Battlestar Galactica Cylon infiltrators.
Basically this would be another really hard mission that would probably only appear when your company is well established. Basically a hostile sentient computer virus beams itself into the ships computers where it will hide in dormant until a crew member or multiple crew are put under surgery (I assume the surgery will be done by some sort of futuristic automated machine?) in the medical bay where it will then activate, slaughter and turn the medical bay patients and turning them into cyborgs under the virus's control. Worst of all the cyborgs can't be detected by just looking at them, you'll never know they're cyborgs unless you have special scanning devices set up on the ship (something like a metal detector that would detect hidden or implanted objects on a person)
The cyborgs will then go straight for the ship's AI core, where they will attempt to hack and bring the ship under the Virus's control. If successful the ship defense systems will turn hostile on your crew: defense turrets will fire on crew, doors will lock and have to be overridden by engineers (who can override the locks) or marines (who can weld off locks or blow the doors open). If you have chemical gasses aboard for defense purposes it will pump those into all areas that it can be routed to. Also after the AI core is infected by the virus a countdown will start, your crew and marines will have a certain amount of time before the virus bypasses firewalls and is able to shutdown life support, food, water supplies, and destroy the engines. All the while the cyborgs will roam the halls and attempt to kill any crew member or marine they come across, then take their corpse back to the medical bay and convert them into cyborgs as well.
The way to prevent this is to not fall behind on medical-bay maintenance, doing often, routine checks on the medical-bay equipment will find and eliminate the virus before it activates. Plus have scanning devices (if those are added) in certain areas of the ship which can detect the cyborgs (or any infiltrator for that matter) and alert the marine garrison and activate all defense turrets on the cyborg before it gets to the AI core. Of course the scanning devices would have to be maintained as well.
Basically this would be an intense mission that would turn your ship against you if it gets out of hand, which it can really quick; but it can also be easily prevented with the right precautions.
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Another thing I think would be great is if your ship is lost to a disaster that didn't destroy it (like one of these sci-fi thriller like disasters I have in this topic), it will leave a marker on the galaxy map showing the location of the wreck. You can later attempt to send another ship to the wreck to salvage. Though this would be hard as by the time you will reach the derelict ship, it would be completely overwhelmed and riddled with whatever took it over (unless it's the sterile man made creature I listed above, then there would still just be one of it roaming the ship).
In most cases boarding the ship would be easy. Basically this would be something of a sci-fi survival horror mission. You would basically board the ship like you would an enemy ship, and you're left up with what to do from there with your assault force. You could attempt to repair and restore power and air if feasible which would allow you to see what is going on throughout the entire ship as well as it's status and hostile life on board. But this would be double edged if you're up against a virus infected AI core as restoring power would give it more control (reactivating defense turrets, infected medical bay and the like) and allow it to see you too and start sending all it's forces in your boarding team's direction.