A quick and very underused technique to create blur effects.
The principle is simple: you create a short animation and, instead of rendering it entirely, just render one frame, which will be your final artwork.
Step 1: you need some parameters to animate. I used a simple plastic with only 2 transforms.
Step 2: Open the animation editor (Ctrl+T or Window > Animation Editor). Set total length to some reasonably amount of time. I use 30-60sec currently, since its short enough to not get lost and long enough to have some room to tweak to control the blurring.
Exposure time controls the amount of motion blur. No worry much about getting the "right" value right now, since you can change it at any point.
Since we are only looking for one frame and not a full animation, there is no need to create many keyframes: 2 usually do the job. If, after making the animation, there are no frames that you like, you can just change one of the keyframes and get a whole new thing quickly. The first keyframe are the default params. For the second keyframe, just move the frame slider all way to the right.
Editor view of the default parameters.
Step 3: just grab the transforms, move them around, rotate and scale (in a way compatible with the parameters you are editing, of course).
So this is how my second keyframe (the parameters pictured above) looks like on preview.
Step 4: Go back to the Animation Editor and move the frame slider around looking for cool stuff. Change the exposure time (i went quite crazy on it this time). Basically, your blur amount depends on both exposure and the amount of changes you made in the parameters.
Step 5: Find a still you like, and render it as you would render a not animated artwork. My result is here:
Just another example: a recolored version of Paisley, with motion blur added using this technique.