I went snowmobiling at 3 and 4 months with both my girls, and still go jogging when I have the energy. You can do some crazy stuff on a snowmobile, but I'm a pretty tame person anyway, so I just did the riding on normal paths...no hill jumping or anything. Some of the trails were REALLY bumpy and jolted me pretty good, but at 3/4 months, it's not a big deal. I would say the same for amusement rides...anything that doesn't drop you really fast, jolt you really bad, or try to mimic Mach 3 (or go backwards, since at 3/4 months you are still feeling pretty nauseous--at least for me) should be avoided. I would think you could still do the tamer coasters, though. If the sign says no preggos, I would tend to agree with it.
Personally, I feel it's a question of what you are used to, but you definitely have to take into consideration the affect that hormones have on your body/joints. (And at this stage, I really think that's what the concern is, unless you've had problems with keeping a baby to term.)