There have been some great suggestions here, I would like to add the following :
Security: Find the hidden bomb ( drill ), To add to the nuetralize the intruder idea: coordinating security teams and using force fields to corner and capture said intruder. Escort the reluctant emmissary ( someone who is in the habit of ditching their protectors). Find the emmisaries lost pet ( yes we all hate this one). Search for the lost item ( datapad, etc ). Shipboard hand to hand combat tournament.
Engineering: "Run the diagnostic" run a scan of epuipment of five areas of the ship for any needed maintenance, Find the cause of a mysteriously overloading eps conduit ( can go hand in hand with the first one). Routine replacement of worn out conduits/circuit boards etc. Damage control drills ( from repairing battle damaged equipment to fighting plasma fires ).
Medical : Find the injured crewman ( perhaps his/her combadge is disabled and the computer cant find the crewman) Emergency triage drills for a ship or colony disaster. Diagnose the patient ( an unknown ailment has afflicted a crewman/passenger. could be a drill or test ). Combat medical teams ( referring to injured personnel in ship combat that require teams to respond to the scene and stabilize victim for transport ).
Tactical: Various ship combat sims, but also running crew readyness drills and getting faster response times.
Recreation: Model building artistic endeavours ( painting : would'nt it be nice to put something up on that blank wall of your assigned quarters? sculpting, also as suggested music. Sports ( Intership olympic games?? ) Designing clothes ( do you always want to wear that uniform on shoreleave all the time? Swimming : racing or relaxing? Public speaking: giving a lecture on the prime directive?
Science: This is a huge area, I'll try and cover this one later.
Mini-games. Hmm.
Well if you look at you characters main tasks, and what to apply mini games for, i could imagine a wide variety of ideas. Some ideas that could be made into mini games IMO:
Operating on a damaged brain.
Ops/Tactical: Find the cloaked ship.
Ops: Scan for lifesigns.
Security: Locate intruder.
Security: Neutralize intruder.
Ops/Transporter crew: Transport away team to <location>.
Command: Away team: shutdown warp core
Engineering: Optimize matter/antimitter reaction
Engineering: Purge impulse manofolds
Engineering: Replace EPS conduit
1st officer: Manage the departments. Tough job.
Captain: Whatever you want to get the job done
Helm: Navigate the nebula/asteroid field whatever
Helm: Evasive maneuvers
Helm: Give tactical a clear shot
Loads of stuff really. And thats just the main tasks, what about the hobbies?
I think that stuff should be full-games, not min-games. Just for the record. Some great ideas, too. Hobbies as many games, jobs as actual deep fun rewarding gameplay, every bit as compelling as combat.
