Software to read PDFs with inverted colors

Evince can invert colors. Use view -> invert colors or the keyboard shortcut ctrl+I. You can then set it to presentation (shortcut F5) if you want it to be full screen.

You can use SumatraPDF, launching it with appropriate command line switches:

White text on black:

sumatrapdf.exe -invert-colors

Green text on black:

sumatrapdf.exe -set-color-range 0x00dd00 0x000000

You can pass any hexadecimal colors (first being foreground color, second background color) and all the contents of the PDF (texts, images, background colors) will be "scaled" accordingly.

Adobe Reader allows you to use a custom color scheme for the document background and text (already suggested by paradd0x). In v9.5, this option can be found in Prefs > Accessibility.

I believe this solution is superior to simply inverting colors as in Evince, as in this case you will often get a very nasty contrast: very white on very black. With Adobe Reader you can however choose a color scheme much nicer on the eyes, such as light grey on dark grey. Such a scheme, similar to that used by Darklooks on Linux, would help reducing eyestrain when reading PDF documents on-screen.