How do I keep my hamentaschen from puddling in the pan?

I agree with everyone who said that cold dough helps. My recipe is similar to a pie crust and it holds together well. I use an egg wash before I fold the hamentashen and that also helps keep them from unfolding in the oven.

I use a cream cheese base (I adapted from the 2 recipes on Smitten Kitchen), which I think makes the dough a little stiffer. I chill the dough in circles on the baking sheet, pre-filling, and then chill them again after filling+folding, before baking. A bit more labor-intensive, but you get into the rhythm if you're making many sheets of them.

FYI: It's illegal and impolite to copy any copyrighted recipe without permission of the holder of the copyright. That's why I am messaging SusanBrooklyn Maida Heatter's recipe.

Here's a cookie dough from my go-to Jewish recipe guy, Raymond Sokolov, (good recipe from Joan Nathan, too, but this one I know I've made):
Hamentashen
2 cups unbleached flour
1 tsp baking powder
Pinch of salt
½ cup sugar
8 tbsp butter (1 stick) – cold, cut into small pieces
2 eggs, lightly beaten
1 tbsp grated lemon peel

Sift flour, baking powder, salt, and sugar in large bowl. Work butter in using a pastry blender. Add the eggs, mixing in with pastry blender. Add lemon peel. Form into a ball and wrap in wax paper. Refrigerate for at least an hour.

When you get ready to bake, preheat oven to 350. Grease a cookie sheet. Roll out dough on floured board to 1/8 to ¼ inch thickness. Easiest if rolling between two sheets of waxed paper. Cut into 3 or 4 inch circles (use a jar top if you don’t have a cookie cutter). Fill each cookie with a heaping teaspoon of filling. Pinch in three corners and fold over to form the triangular shape. Brush dough with egg wash. Bake on cookie sheet for up to 30 minutes but check for doneness at 20 minutes. It is done when they look light brown and crispy. Makes about 30.

@ChefJune, I'd love to get a recipe for the cookie dough base.

I think the problem of the cookies not keeping their shape comes from the fillings and not from the cookie itself. I use an old sugar cookie recipe and then fold it up, but if you aren't using fairly dense fillings, the cookie will very likely spill over. Regular store-bought jams have too much water and sugar in them to stand up to the baking; traditional lekvars (and nutella) don't spill over.

Are you using a cookie dough or a yeast dough? I prefer the cookie version in which case, as ChefJune says, you need to chill the dough.

What filling are you using? Is it wet? It should be more of a thick paste. I used to make them with Sunday school kids and we never had a problem - even with heavy handed little bakers. I'll look for a recipe.

Here's a recipe from the site. I think I'm going to try it today, in fact. I agree with ChefJune--the secret to cookies holding their shape is keeping the dough cold.
http://www.food52.com/recipes/4239_hamantaschen

I have always used Maida Heatter's cookie dough base, and I chill the shaped cookies before baking That way they hold their shape nicely. Towards the end of baking, I don't give all of them enough time in the freezer, so the last tray (or two) sometimes come out flatter, but I would never describe them as "puddled." If you need a copy of her dough recipe, let me know.