Recs.
Updated
Adobe Photoshop is undoubted leader in graphical design, digital art and painting. Could be easily adapted to draw pixel art.
SpecsUpdate
Pros
Pro Packs a staggering amount of functionality
Photoshop is the most fully featured image editing software available today allowing you to perform highly advanced image manipulation.
It has tools for RAW image adjustments, lens correction, retouching, image stitching, HDR, fixing framing. It supports most professional color modes and file formats. It includes extensive lists of filters, styles, effects, fonts as well as tools for painting, sketching and typography work. It understands both raster and vector graphics. It even includes tools for video editing, working with 3D objects and support for 3D printing.
Pro Industry standard
Photoshop knowledge is easily transferable across game development art jobs, and this is by far the most popular tool of 2D artists. It is used by professionals everywhere in a wide variety of fields including photography, graphic design, and digital art. In that sense, you won't be alone when using Photoshop.
Cons
Con Latest versions of Photoshop are subscription-only
While you can still buy CS6 from 2012 without needing a subscription by contacting Adobe support or the cut-down Photoshop Elements, any full-version version of Photoshop past CS6 requires a subscription.
Con Asset management capabilities are lacking
In Photoshop asset management is done through a separate program called Bridge. As Bridge is supposed to be a file management tool for not just Photoshop's files, but for files generated by all of Adobe's applications it covers a breadth of capabilities, but not depth.
Con Learning it can take some time
While you can relatively quickly learn how to perform a few basic image editing tasks, understanding Photoshop's ins and outs can be difficult. It's partially due to the sheer amount of functionality that Photoshop packs (and understanding that some of the advanced functionality can take a while to understand on its own), and partially due to it being aimed at professionals with little hand-holding for novice users.