Answer:
AI files are readable only by adobe illustrator and contain exactly one color --usually black. They are also referred to as vectors. To convert this file, open it in Adobe Illustrator (there is really no way around this part that I have discovered, though I have tried.).
Since I am most comfortable with image editing software like Photoshop and GIMP, I choose the "cut and paste" method into one of the aforementioned programs. This will usually not effect the quality of your image.
Once inside of your image editing program, it needs to be flattened and the transparency needs to be eliminated. To do this the long way, you can add a solid background and manually flatten the image. To do this the short way, save it as a jpg and your editing program will alert you that the jpg file cannot handle transparencies. Select that you are alright with this and your software will automatically add a white background and flatten the image before it saves the file.
To retain the transparency, try saving it as a gif, psd (photoshop only) or an xcf (GIMP only).
Correction:
Adobe Illustrator files are frequently more than one color, although certain programs, such as GIMP (perhaps) may not be able to read all of the file data.
You can convert from AI format to jpeg easily by opening or importing the AI file into Adobe Photoshop, or any other raster-based (pixel-based) program that recognizes the file extension. The image will automatically convert from vector to pixels when opened, and you can then save it as a jpeg.
If you have a more current version of Illustrator, you can "rasterize" or "flatten" the image and save it as a jpeg directly in Adobe Illustrator. Always use the "save as" option to preserve your original (vector) file.