Some cake recipes say to use a bundt cake pan instead of a regular round pan. What would be the requirement of baking a cake that would make a bundt pan better? Is it a thicker batter, heavier/denser cake? Or is it just looks when you don't want a couple of 2" high layers?

I understand that the hole in the center gets the middle of the cake cooked and you're usually looking at a 3 or 4" high cake, but what is it about a particular cake batter that would make this necessary? And can cake batters that "need" bundt pans also be baked in a regular one or is that just looking to get a cake with an uncooked batter center?

Alton Brown, where are you when we need you?!

Not realy sure about special batter, but I know that if your going to follow a recipe that gives baking times for a bundt pan, you'll need to change that for sure. Probably take longer. My guess.

Usually the batter used for a bundt cake, is a more dense batter. Doesn't mean you cannot do the same cake in a regular pan, it works well in some cases. But often a bundt cake that uses a cake mix as a base, will have less oil, an extra egg, perhaps some sour cream in it or a pudding, something like that.
I have a few recipes meant for an angel food pan or a bundt pan, that also work well in a regular pan. But some cakes really do cook better in a bundt pan, when that is what is called for. I like the Williams Sonoma recipes and I love the Nordicware Bundt pans. I often use an angel food cake pan instead, if I have a lot of these types of cakes to make at one time.
Yes, the cooking time will vary quite a bit when you use regular pans instead.
Hugs Squirrelly