A free program that allows me to make interactive images? For example, if you click on a certain part of the image, something happens.

It's not possible to do that. The closest thing to that is a Flash swf. To do what you described would require the cutting up of the particular image then have scripting added to it to do different things. A program that I can think of at the top of my head that can do this is Dreamweaver which is not free. However, Dreamweaver is a tool so it is not necesarily needed to achieve this so it is possible to do this on your own without a program.

There could be a free program out there that does something like that though, so I recomend you search around.

Yeah, that's what I was thinking. I have searched around, but to no avail.

If you cut up your image file with any image editing software, and script it using a HTML editing program you could do it. Theres plenty of freeware of that.

Flash.........................
http://www.click-now.net/download/Macromedia_Flash.htm

Stop being annoying.

Do you want an animation to happen or just to split an image into links?
(if you want to split an image into links, try this http://www.download.com/TomaWeb-Image-Mapper/3000-2381_4-10149948.html?tag=lst-3&cdlPid=10149949)

Otherwise, steal flash.

Of course you COULD make the link take you to a page with an easytoon animation by you, but that all seems a bit 1995 to me.