I have a
Canon Powershot SX120IS. There are more recent versions of this camera, but they are all pretty similar. It's only a point and shoot, but it stays small and that allows me to take it on rides with me (I never actually take any photographs or video on the ride) since I can easily fit it in my pocket or have it in a small back attached to my belt (no it's not a fanny pack). This work at every park I've been to except Indiana Beach; they have the strictest interpretation of loose articles I have ever encountered. This camera also takes some amazing photographs if you know how to set it up with the manual settings. If it's a nice day out, you really can't do anything wrong (except have the ISO too high). If it's too bright or dark, then you may have some issues if you're not experienced. I'd think this would go for any camera with manual operation. I've taken some amazing pictures all over with this and love the camera. One problem I have with it though is that the photos get really grainy if I use ISO400 or higher. This really isn't a problem at parks though, unless it's dark outside. I've only had that problem at arenas like the United Center. I've read some things that say the ISO problem has to do with the Canon hardware, and that other brands like Nikon seem to be better.
As for some simpler stats, the Canon Powershot SX120 IS is a 10 megapixel camera with 10x optical zoom. I prefer optical zoom since it actually magnifies the subject, and doesn't simply make the pixels larger like a digital zoom would. The auto settings are ok on this, I wouldn't use them at the parks though. I like to be able to control the shutter speed and aperture myself.
Pros of my camera: Small size allows you to bring it on rides, takes AA's, so you can just buy new batteries at a gift shop, and optical zoom.
Cons: Can't really shoot ISO400 or higher (this camera can go up to ISO1600, but I've never done it)
This is a good camera to start out with if you're not sure how to use something with more complicated settings.
If you have the skill, money, and want to use a day for only taking pictures, then I would go with a SLR. So much more power and the ability for better pictures. The only problem I'd see with the SLR as others have pointed out is the size. This is definitely too large to bring on rides, and I wouldn't considering the cost of an SLR.
If you want, some samples of my pictures:



Extended exposure (probably about a half second) of the Orbit.



Obviously not a park picture, but I wanted to demonstrate the problem with shooting at higher ISO speeds in low light. This image was adjusted in Gimp to fix some of the brightness issue.

Also obviously not a park picture, but just a cool one I like to show.
I also have a PTR from Cedar Point, about August 2010 that is floating in the catacombs of the Trip Report forum that has more photos taken with this camera.
Director Guy, those are some awesome pictures you have there as well.