There are two kinds of walls: bearing walls and non-bearing walls. You can do anything you like to a non-bearing wall. But if you remove or even cut open a bearing wall, you can literally bring down the house. Check the joists or rafters in your basement or attic. If they run perpendicular to the wall in question, it’s almost certainly a bearing wall. If they run parallel, it’s probably not.
For more on walls, consider: