There are a ton of different image editing program out there that do numerous things. But there are even less which support creating and editing layers, something which was popularized by the likes of Adobe.
These programs support editing graphics and their layers.
GIMP is an open-source and free Photoshop alternative (for Windows).
GIMP for Windows can add text to an image, apply special effects to a picture, view EXIF data, create animated GIFs, create PNG graphics, create web graphics and create and edit layers.
Advanced, yet powerful image manipulation suite acting as the open-source standard for creating, modifying and printing images with plethora of filters,...
ImageMagick can add text to an image, apply special effects to a picture, create PNG graphics, create web graphics, create and edit layers and batch process images.
A highly recommended freeware vector graphics editor that's packed to the brim with features to edit objects, work with layers and activate effects.
Inkscape can add text to an image, view EXIF data, create PNG graphics, create web graphics, optimize graphics and create and edit layers.
Free paint software for creative artists and amateurs with a number of drawing tools, image enhancements and effects for creating digital art.
Krita can add text to an image, apply special effects to a picture, create web graphics and create and edit layers.
Legacy version of a popular graphics editing program with support for photos, web graphics, drawing and various other tools by Corel.
CorelDRAW can add text to an image, apply special effects to a picture, create animated GIFs, create PNG graphics, create web graphics and create and edit layers.
Graphics editing application with a collection of rich tools for artistic creations, filters and layers.
Artweaver Free can add text to an image, create PNG graphics, create web graphics and create and edit layers.
Portable Windows version of the popular free image editor GIMP.
Portable GIMP can add text to an image, apply special effects to a picture, create web graphics, optimize graphics, create and edit layers and convert RAW to JPG.
An advanced image editing suite supporting vector, 3d, filters and more.
Xara Designer can optimize graphics, create and edit layers and convert RAW to JPG.
Powerful raw image editing utility that converts, tunes and edits raw images from your camera and can export them as beautiful JPG files.
Photivo can apply special effects to a picture, view EXIF data, optimize graphics, create and edit layers and convert RAW to JPG.
A lightweight paint program which supports digitizers.
Speedy Painter can apply special effects to a picture, create web graphics and create and edit layers.
Digital paint program with pressure support and custom brushes.
MyPaint is software which can create and edit layers.
Hornil StylePix is a free image editor with a number of advanced features.
StylePix can apply special effects to a picture, create web graphics, optimize graphics and create and edit layers.
Graphics and image editing suite, based on layers, which can apply various filters, color optimization and special effects with additional advanced...
Pixelitor can apply special effects to a picture and create and edit layers.
Award-winning image editing suite with professional digital imaging tools, effects, filters and plug-in support powered by the Mercury Graphics Engine.
Photoshop CS5 can add text to an image, apply special effects to a picture, create web graphics, optimize graphics and create and edit layers.
Versatile, professional photo and image editing software.
Focus Photoeditor can apply special effects to a picture, optimize graphics and create and edit layers.
A graphics editing suite with many useful tool and features.
Saint Paint Studio can add text to an image, apply special effects to a picture, create PNG graphics, create web graphics and create and edit layers.