Although it's not what you are looking for, you do not need to do any programming to make simple animations. All you need is a graphic editor that does objects/layers. You create objects such as text, shapes, multi-object cartoon figures and use stop animation. You save a picture (which will become a frame), move the objects, save that picture (the next frame) and so on. When you are done (many hours later!) you can sequentially number the pictures and load them into something like freeware VirtualDub. That can create an avi from the frames. You can drop them into any video editor as well. For a small number of frames, you can create an animated gif.
I use part of the above process to apply effect filters that are only available in graphic editors, to video. Extract frames, apply filter(s), reassemble video.
With scripting (which is programming) you could automate some of the process. Decent graphic editors come with scripting (eg Python(?) in Paint Shop Pro, VBA or CorelScript in Photopaint).
You can also use Flash for making animations (and really annoy people surfing your website).