What is a good, free program that makes image backgrounds transparent?

I'm looking to crop out the model of this vehicle in fine detail.

http://pictures.topspeed.com/IMG/crop/20…

I want to use it for a wikia which requires avatars to have transparent backgrounds (background of the avatar is "clear" and shows the wikia's background and color as its background).

Does anyone know of a program which allows me to do something like this in an easy manner?

First off, you have to keep in mind that, without layer information preserved, your computer has no idea what part of the image is 'background'. it has no high-level visual processing system that can define the 'background' as different from any other part of the image, the way the human brain does. And even if it did, different systems might define it in different ways.

That said, there is some amount of free image manipulation software that can help you do what you want to do here. I would suggest GIMP:
http://www.gimp.org/

I use photoshop it's almost free in my country :)
anyway i fixed the picture you attached to this topic, you can download it in gif or png format via this links:

http://4syrians.com/images/agera.gif
http://4syrians.com/images/agera.png
http://4syrians.com/images/agera24.png