The best free and commercial programs we can suggest for using when creating, editing graphics (images).

Photoshop – commercial
Adobe Illustrator – commercial
Gimp – free
Krita – free

Photoshop is most popular and versatile program for creating, editing and saving graphics. Its not free but very popular among web and graphic designers.
Adobe Illustrator – suitable for digital artwork because it allows saving your graphic at best quality as vectorial images. Also commercial.

Gimp – well known alternative to Photoshop but free.
Kitra – free and open source . Personally I did not intensively test this program but as far as I did, I was impressed by it’s options, resources, workflow, UI structure. Also tested with graphic tablet and on my system does not work pretty well with pen sensitivity but it’s my first choice when it comes to 8bit pixel art.

Among graphic software I’ve also tested Autodesk SketchBook Express 6.2 (which was bundled with my graphic tablet) and I was impressed by the intuitive UI. Because it works with layers, it is suitable for digital artwork and less for photo manipulation