Someone back in the day on STOnet asked this.

Care to refresh our memories on some of the ideas...other than the above.

In addition to the board games we've seen the series, I think the Holodeck should allow access to a host of minigames, as presented above.  I should hope it will be useful for just such diversion, as well as being useful for reviewing/redoing missions.

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 point at Fable 2. In August they will be releasing three gambling games early for players to earn (or lose and gain massive debt and death threats) gold to be transferred over when the game launches. once the game is launched, these games will become multiplayer (or remain single) over XBL.

Now i am not saying that STO needs to release playable content early, but what i am saying is that it can be done. It may not be at launch, but it should happen eventually. Even SWG had a crude gambling game, and slots (which i do not consider gambling, just a money sink hole. the chance to win is less than 5% :P)

 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.