There are several very good programs out there. The next question is how much do you want to do with it.
Cropping and fixing red eye can be done with almost any freeware.
Adobe Lightroom is basically a digital darkroom which allows you process photos for exposure, white balance, minor touchups etc, but not real heavy photo manipulation. Photoshop Elements is a scaled down version of the main program(much less expensive that full PS). And then Photoshop. If you're looking for professional software, Photoshop is probably the way to go. If you're just looking for basic photo program, check out ACDSee or 5DFly photo design. It's a great program for a great price.
Related knowledge of photo editing software:
What is image layer - the basic knowledge to editing photo
How to Add Borders To Your Photos
Price list of photo editing software
Price of photo editing software
photo editing & printing basic
Question of how to resize image on a forum
Add a Watermark to a Photo in Corel Photo-Paint
Articles about add watermark on photos
Photo Sharpening Software and Plug-ins
How to batch resize the pictures
Would you like to learn more about photography & photo editing?
Printing a photo requires editing?
Why is it Not good to Resize, Rotate, and Crop Graphics in Microsoft Word or Excel?