GIMP (GNU Image Manipulation Program), the open source alternative to Photoshop can be downloaded as a portable version. However, due to being portable, the choice of fonts you can use is limited by what is on the operating system and part of the basic GIMP package, so if you use the font tool and choose a font that is not on another system, you may have problems. Thankfully, fonts are easy to copy (you can copy them from the Fonts applet in the control panel by just dragging them to another folder).
To make your fonts available wherever you use GIMP Portable, you just copy them to
E:\PortableApps\GIMPPortable\App\gimp\share\gimp\2.0\fonts (where E: is the drive letter of your portable drive). Then you can go on any Windows PC (even without Office or OpenOffice installed) and still use your own fonts (those which you are licensed for).