Drawing stick figures---simple lines and circles---is the simplest form of animation. You can find several free programs that allow you to create stick figure animation, including Pivot Stickfigure Animator, Stykz and This Is Stick Figure Animation Theatre (TISFAT). Pivot and Stykz each use a simple interface and let you build figures "from scratch." TISFAT is a downloadable program with more options than the other programs. With TISFAT, you can save creations as GIF, BMP, Flash and AVI movie files.
DigiCel FlipBook, a 2D animation program popular with both amateurs and professionals, makes it easy to perform such functions as storyboarding, lip-syncing and cleaning up rough drawings. Toon Boom Studio 4 lets you either create images within the software or import them. Novices may prefer starting out with more basic programs such as Animation-ish or Pencil---a free program usable on Mac, Windows and Linux that allows the use of both vector and bitmap images.
Although typically favored by professionals, some 3D animation creation programs have made this format popular with amateurs too. One free downloadable program, Blender, works well with both Windows and Mac platforms. Blender includes such features as fast skeleton creation mode, mirror editing and reflection maps. Anim8tor, another free program and a great introduction to 3D animation, allows you to create and modify 3D models and characters. However, this one is currently only available in Windows.
If animation creation using just a computer doesn't interest you, try adding a digital camera to the mix. The Mac-only animation program iStopMotion lets you create flip books, time-lapse recording, composites and chroma-keying---all with digital photos. The program also comes with keyboard and voice recognition shortcuts. Morpheus offers a suite of three software packages (distortion, morphing and compositing) that enable you to create some highly unusual animation with photos. The suite includes 15 sample animations.