Recs.
Updated
Photoshop is the most popular photo editing software around. It is the industry standard today and is used by professionals and hobbyists alike. It is fully featured and allows for an extensive amount of photo editing jobs to be done.
Specs
Pros
Pro Industry standard
Photoshop is used by professionals everywhere. It is taught in classes, used by artists and is even used by medical professionals. If you've seen a magazine ad featuring a model, you've probably seen the effects of Photoshop. You won't be alone when using Photoshop. The internet is full of tutorials and videos on how to use Photoshop. This fact, coupled with the trove of plugins available for Photoshop means you can use it it to make the professional looking or artistic images you need.
Pro Fully featured
Photoshop is the most fully featured image editing software available today allowing you to perform highly advanced image manipulation.
On top of that it offers features beyond the realm of typical image editing software tools such as support for video editing, 3d elements and 3d printing among others.
Pro Mobile companion apps available
There's a free mobile app available for iOS, Android & Windows Phone.
Cons
Con Expensive
For a high-quality product, the price is high enough to match. With the new Adobe model, all Creative Suite Products are subscription based only. This means that for the complete "Creative Cloud" you are required to buy a year subscription for about 600 USD. In order to use just a single product, its a $20 monthly subscription. The cheapest option would be Photoshop Elements 12 which is a single time payment of less than 100 USD depending on where you look.