I had asked question like this long ago at WPTavern and it fizzled. Hope it fares better this time. :)
Drawing graphs can be done with multiple methods (generating image files, JS, Flash) and there are a lot of libraries available overall.
However there are some specific factors in context of WordPress:
it might be efficient to use lighter library with dependency on scripts bundled with WP (like jQuery);
it needs to be licensed under GPLv2 or compatible to fit in official repository (note that it has more harsh requirements than WP itself);
What libraries or other solutions had you used to build graphs in WordPress?
Please one thing per answer, so it is easier to discuss and vote on.