Here are a few traditional tutorials from the Angry Animator.
Lesson 1: The Bouncing Ball - This is the first lesson taught to an animation student. This tutorial breaks it down into a simple series of steps, and shows the basics of flipping and rolling paper.
Lesson 2: The Walk Cycle - Most people can't wait to make a character walk. It's advanced, but I've tried to simplify it, showing the 4 main poses of a walk cycle, and how to build the walk around them.
Lesson 3: Dialog - A very simple approach to creating effective dialog, using only six mouth shapes.