BarbaraMB:
I think it'll depend what kind of camera you have - how big it is, what type of viewfinder you've got, if it can handle the action. A few years ago, I taped Big Thunder using a regular viewfinder, up to my eye, and it was pretty darn difficult. You really risk losing an eye!!
I managed to do it, but my most recent venture was much more successful. My new camera has a side screen and is a bit smaller than the older one - it's a Sony...418? Something like that. ANYWAY....
If you have the side screen, it's a bit easier to hold it steady with two hands, and ALWAYS with the strap around your neck, and just keep the corner of an eye on the screen so you know you're not getting only the back of someone's head. If you get daring, you can try gripping the camera with one hand, but it's steadier with two. I reccommend finding some sort of focus point (like the first car, the shoulder of the person in front of you, etc.) and keep it in the shot so you have a reference when you take a quick glance to make sure you're getting the ride.
If you want the "experience" of being on Big Thunder, which I did, I'd reccommend taping with just a corner of the train in the frame so you can get the rails and scenery in. It forced me to keep the lens steady and now is a virtual ride on Big Thunder whenever I need my fix!!
Splash Mountain - yep, like Mia said, it's easier than Big Thunder. You're fine until the final drop, then it's all up to reflexes and fate. I've had pitch darkness in some tapes, splashes in others, WAVES of water in the last one. They're all fun to watch though!! (Especially to hear my sister squealing at the wetness!!)