While it is a commercial program, I find it outstrips all open-source solutions in both usability and speed - at least for my uses. And they have quite good Linux support, including .deb-packages and simultaneous releases on all platforms.
Pinta is a drawing/editing program modeled after Paint.NET. It's goal is to provide a simplified alternative to GIMP for casual users. It is currently early in development.
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I have been quite happy with using Bibble 5.
While it is a commercial program, I find it outstrips all open-source solutions in both usability and speed - at least for my uses. And they have quite good Linux support, including .deb-packages and simultaneous releases on all platforms.