Motion blur is just what it sounds like: a blurring effect, produced by motion. Depending on how the effect works, the background around a moving object can blur, the moving object can itself blur, or it can simply leave a blurry trail behind it and yet be perfectly visible. This third option is all that JJ2 will allow.
Motion blur in JJ2 makes use of the fact that in single player, if there is no background, everything will remain drawn to the screen and thus leave "trails". By themselves these trails are not motion blur, as they are perfect copies of the original graphics. However, there are four ways to exploit this phenomenon to get something somewhat closer to true motion blur:

Method 1: Transparency
The simplest way is to have layer 8 be fully transparent. (And untextured.) The drawing to screen of the transparent tiles almost completely covers the trails, but a little shows through. However, this little is incredibly limited and the motion blur provided by this effect is almost invisible unless you pause/screenshot the game to look for it.
PROS: Very simple, can be applied to most any untextured background.
CONS: Barely visible, requires that hardware acceleration be off.

Method 2: Moving Holes
Brought to my attention by Jerrythabest. Simply take a tile such as the one below, put it in layer 7 with Tile Width and Tile Height on, give Layer 7 some automatic speed (Jerrythabest uses 0.299988 for both x and y, so it always moves up and to the left), and you're set to go. Graphics will not actually color fade away, but they do appear for only limited periods of time and it does look kind of cool.

PROS: Very simple, quite adjustable.
CONS: Takes up layer 7, doesn't work too well with backgrounds that aren't essentially just single colors, requires high detail.

Method 3: Water
Leave the background empty (or if not empty, at least let the black void show through), and go underwater. Everything will be updated strangely and the ground will leave trails that shift around in the watery currents. This effect looks different in 8-bit and 16-bit color but more or less works in other.
PROS: Simple, looks very good in 16-bit.
CONS: Requires that the level be underwater, requires high detail, and can look pretty weird in 8-bit depending on the tileset.

Method 4: White Glow
As always, leave the background empty, but this time change the level's lighting to something brighter than normal. This will cause a transparent white sheet to be constantly drawn on top of the whole level, thus gradually obscuring trails from view. The best setting I have found is Intensity 127, Red 0; trails become completely erased in 16-bit color, and the whitening of layer 4/etc is not too intense. 8-bit will always leave slight trails no matter how bright it gets, though.
PROS: Simple, leaves very good motion blurs.
CONS: Isn't quite perfect in 8-bit, requires that the level have a white background, requires that the level be brightened, requires hardware acceleration to be off and ambient lighting to be on, and for there to be no water in the level.

None are perfect solutions. And none work in multiplayer, except temporarily when there is a large amount of chatting onscreen. But they're what we've got, and one of them may somehow be just what you need someday.

Added on: 13 August 2006 01:36. Made by Violet CLM.