I too was on a quest to find out how to get the most background blurs in different situations. It turns out that in the quest for blur, you can oversimplify by dividing into 2 type of blur: depth of field, and background blur. Most people concentrate on the depth of field which is almost entirely determined by f-number. As Big Mike said, moving closer gets you more blur (less depth of field), but you'd have to use a lower focal length to accomplish the same field of view. The lower focal length gives you less blur from a larger depth of field, so the distance and focal length issues almost exactly cancel each other out leaving f-number as the sole (almost) variable in depth of field. If you don't believe it (I didn't at first), use any online depth of field calculator. Make sure when you double the focal length, you also double the distance to subject to achieve the same framing of the subject. This will give you almost EXACTLY identical depths of field.
Turns out the blur we're mostly looking for is the background blur. "Background" can be loosely defined as anything beyond twice the distance from the subject to the camera. The easier way to think about it is that you have to be at least as close to the subject as the subject is to the background, preferably closer. The amount of background blur is determined by aperture, not f-number. Since most people confuse the 2, aperture is focal length divided by f-number. So a 50mm lens shot at f/2 has an aperture of 25mm. Larger apertures produce more background blur. Generally speaking, longer focal length lenses usually are capable of larger apertures than shorter lenses, but that's not always the case. For example, 300mm divided by 5.6 = 54mm, more than twice as much as the 50mm at f/2. You'll have to do the math with the lenses you have.
So one would deduce that you should always use your longer focal length lenses if they have the largest aperture. Not necessarily. The problem with this is if you choose a long focal length lens and you have to back away pretty far from your subject to properly frame it, you now risk having the background closer to your subject than you are. Now the background is no longer the background as defined above, and will now more closely follow the rules of the depth of field blur. This is a problem because most long focal length lenses do not have low f-numbers meaning there will be a deep depth of field, therefore ruining the blur you're looking for.
So to summarize you want to choose the largest aperture lens that still allows you to be as close (or closer) to the subject than the subject is to the background. That's how to get the most blur. If your background happens to be really far away, you can blast away with your long focal length, high aperture lenses. As others have said, bokeh is another subject altogether.
the word bokeh is the English translation of boke which means "blur". However in photography it's generally referred to as out of focus quality. Which I just looked up is boke-aji "blur-quality".
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