In the files marked "Stuff I'd like to run sometimes", there's one entitled "CSI: Greyhawk". The actual town isn't important (Sharn might be better if I knew diddly about Eberron), but investigative adventures ALL THE TIME feels like it could be fun.
The PC:s would be officially empowered to investigate crimes, either as part of the legal system (probably more Eberron/Forgotten Realms) or as the Queen's Finest, yadayada. Whatever, people die, there's a crime scene, characters use their various abilities to find clues leading them to the badguy and kick his/her arse.
So what system would I use for this. D&D 4E is nice with its skill challenges, and rituals if mere skills fail the PC:s. I've even considered a twist to skill challenges: The PC:s would be able to use any skill they want, letting them spam their best skill if they prefer that, but only the first success with any given skill gives them an actual clue to work with. This would encourage using different skills.
However, I'm seriously considering 3:rd edition. Let the spellcasters worry about picking utility spells or fighty spells. Rogues get to use their skills. There will be enough fights that the fighters aren't completely useless, but frankly, I'd boost their skill points and skill lists for a campaign like this. As written... I suppose they could Intimidate suspects.
There are of course systems like Gumshoe that are written specifically to handle mystery games well, but what's the fun in that, eh? Still, don't be afraid to steal ideas from there.