This isn't specifically a motorized bicycle mod, but I think it's a worthwhile [and not often talked about] idea.
This Instructables.com entry gives instructions to making your own bicycle sidecar!
I'm not sure how safe it would be to have another person in this car, but for areas with low traffic, it may not be a bad idea! Even better, you could mount a cooler on the trailer and start your own mobile ice cream business! What better way to pay off that 66cc engine than by using a little engineering to turn it into profit!
You may be wondering if this would legally disqualify your bike as a motorized bicycle: Well, this can depend on the laws in your area, but usually bikes with 3 wheels still qualify, which is what's excellent about this mod! I'd love to see someone do this with a motorized bicycle!
A warning to those looking to mod their motorized bicycles:
Most, if not all, of the hacks and mods featured on this site were made by individual hobbyists. If you are new to working with 2-stroke bicycle engines, please by aware that there's a possibility that a mod featured on this site could seriously damage your engine. Please don't try any mod from this or any other site unless you fully understand what you are doing. The owner of this blog will not be held responsible for both material and bodily damage caused by performing a modification featured on this blog. Also remember that opening up your engine may void your warranty!