Check your shift rod adjustment first.
Below is a link to a parts page depicting the shift rod components. It is highly possible that the jam nut (item #39) has backed away from the adjustment nut (item #11) and allowed the shift rods to become misadjusted.
http://www.boats.net/parts/search/Honda/Outboard Engine/2003/BF40A3 LRA /WATER PUMP/parts.html
You can locate the shift rods and nuts by looking for the access opening between the extension case and the gearcase looking from the front of the outboard. All adjustments are supposed to be made with the gearbox and linkage in reverse gear position. Since you can't achieve reverse, you may need to unscrew the adjustment nut all the way up on the upper shift rod until it comes off of the lower rod. Once the upper and lower shift rods are separated, you can shift the gearbox into reverse by grasping the lower rod with a pair of pliers and, while slowly turning the prop, pushing down on the lower rod. It should sort of "pop" into gear.
Once the gearbox is in reverse, make sure that the linkage under the hood is also in reverse. Sometimes, it is best to take the shift cable off of this linkage as aliboy suggests. This allows you to check for cable to linkage alignment after the transmission linkage is properly adjusted. Either way, you must have everything in reverse.
With the gearbox in reverse and the upper linkage in reverse position, you are ready to make the adjustment. Start by positioning the jam nut 3/16' from the end of the lower shift rod. Then, reconnect the adjuster nut to the lower shift rod, bringing the two rods back together again. Turn the adjustment nut on the threads until it just makes contact with the jam nut. When the nuts are in this position, lightly tighten the jam nut and check that the outboard shifts from reverse to neutral to forward and back consistently several times. Again, it is best to do this with the engine running in a trashcan full of water to simulate actual conditions but it can be checked dry if you rotate the prop while shifting.
If you find that the outboard doesn't shift exactly right after this "initial" setting, you can move the adjustment nut up or down slightly to achieve a smooth shift between gears. When you have it shifting properly, torque the jam nut FIRMLY against the adjustment nut to prevent it from backing off again.
One mistake many boat operators make when shifting an outboard is that they do it slowly, allowing the clutch dogs to "skip" off of one another making a sort of grinding, thumping sound. This action prematurely wears the clutch out. Always shift your outboard from neutral to forward or from neutral to reverse "smartly" in a quick motion to force the clutch to engage without "skipping".
Good luck and let us know what you find.