In order to make a thick cookie you should make sure you are using enough flour and baking soda. Also make sure the baking soda is fresh.

Old baking soda is a recipe for cookie pancakes.

You can also try putting the batter in the fridge for 1 hour before baking so that the dough flattens more slowly.

This recipe makes fantastic cookies. The real trick is determining optimal cooking time for your equipment. We bake these cookies, one tray at a time, for 6 minutes and 20 seconds (the bottoms should be a nice golden brown and the tops are thinking about splitting.) After cooling, the result is crispy on the outside and delicious meltiness on the inside. A nearly perfect cookie.

Jacob's recipe above is a good bet. Mainly because it's a combination of butter and shortening. All-butter cookies tend to spread out more and become quite flat. Shortening tends to be hydrogenated so they have air whipped in which helps with the "lift" of your cookies. Shortening also remains a solid and doesn't melt at room temperature like butter does.

If you like your butter, just make sure that when you cream the butter and sugar, you try to incorporate as much air in it as possible and that it's nice and fluffy. The volume of the butter and sugar mixture should double, full of air pockets. If the butter starts to melt, stick it back in the refrigerator until it solidifies again and re-beat.

Also second Jacob's recommendation of removing them before you think they are done: the tops should just begin to split. Each oven is different so it's possible that you need to check on the cookies before the recommended time to make sure that your cookies don't overbake and become harder than you desire.

RonaldTriangle's tip on chilling the dough should help the dough from spreading too quickly, especially if you are using an all-butter recipe.

Do you live in Arizona by any chance? I lived in arizona for 10 years and I had the flat cookie problem for a while. I fixed it by adding 1/4 more flour to my cookie recipes and cakes.