The FBI would be a great place to try and get into if you want to do investigation. I don't know if you would be a "private" investigator, though. But as I understand it, most PIs start out working for some official organization like the FBI or the police before going independent. It kind of gives you better credentials.
Anyway, I can see the association between adventures and private investigating, but as others here have pointed out, there is a huge difference between detective work in games and real life detective work. The danger is certainly an element that would be more significant in real life, but some of the people here may be overstating it a little bit. A lot of investigation, especially private investigation is going through records and stuff like that. As an example of something a PI might be working on, a lot of investigators are hired now to find out whether somebody's spouse is having an affair. Stuff like that.
So to get to the point, you should only go into investigation if that's what you really want to do, not just because you saw it in a game (even though that may be what draws you to the field in the first place). If you're serious about going into detective work, you might want to check out this link:
http://www.bls.gov/oco/ocos157.htm
mag
