Monkey bread generally cooks in a bundt cake pan to make a donut-shaped cake that is easy to pull apart. This doesn't mean you can't use other pan types, though. Some pans work better than others, but you should be fine as long as you can fully cook the bread in the pan.
The bundt pan creates a donut-shaped cake, whereas a circular pan creates a thick, circular cake of monkey bread without the hole in the middle. The monkey bread may need a little longer in the oven, though, to thoroughly cook the center. In a bundt pan, the pan cooks the sides as well as the hole in the middle; a simple circular pan does not have that same feature.
Square Cake Pan
A square cake pan deviates greatly from the traditional shape of monkey bread, but it is just as delicious. Much like the circular pie pan, you must monitor the center of the bread in the square cake pan carefully to ensure the bread cooks evenly. You can thin out the dough for the monkey bread along the bottom of the square pan, making it less thick than the traditional monkey bread from a bundt pan.
A bread pan can produce a tall loaf of monkey bread, depending on the amount of dough you place in it. The bread loaf pan bakes the monkey bread in a way closer to that of baking bread. The bread comes out in a tall, wide loaf without the circular shape. The bread loaf pan may cause the center of the bread to sag a little, though. The bread gets a little dense at the center of the pan, which causes it to flatten slightly in a long, slender pan.
Spring Form Pan
A spring form pan is generally a circular pan, but can come in other shapes. These pans make it easy to separate the monkey bread from the pan because the sides of the pan separate from the bottom. This lessens the chance of breaking the bread as you try to take it from the pan. This is especially important for monkey bread since it is already prone to falling apart easily. Just slide a butter knife around the edges of the pan to separate the bread from the edges. Monitor the cake carefully during the cooking process, though, because the glaze may leak out.