A couple months ago the family packed into a minivan and headed to SoCal for a Disneyland adventure. I think I'm still recovering. The trip came at the behest and expense of my mom and stepdad, who are far, far braver than I am, and at the end of the day my kid had a blast. Therefore my first tip for how to save money at theme parks is: see if the grandparents will foot the bill. However, if that isn't an option, here's a list of ways to hang on to the almighty dollar while chasing after Mickey or another giant costumed freak.
Some of these tips boil down to carrying enough clothing that you'll wish you had a pet pack mule to accompany you. I'm going to second one tip in a big way: bring your own snacks. Not just because you'll end up spending three dollars for a bottle of water and five for an ice cream. It turns out that the food you can get at most theme parks is naaaaasty. More salt than a gallon of ocean water, heavy on the preservatives, and generally designed to make you feel barfy afterwards. I know I get the "duh" prize for not realizing how bad theme park food would be but since I think I like junk food, I wasn't prepared for how crappy I'd feel. Along those lines, I'll also second "don't overstay" for cost-cutting and sanity reasons. Because crying at the Magic Kingdom just feels bad.