Here's one we can hopefully have some fun with. There is plenty of functionality we can extract from our mobile devices, and accessories can add to that. Some in ways that the phone manufacturers themselves may have never dreamed of.
So, sales professionals and mobile phone power users- what's the weirdest or most unconventional accessory you've ever used with, on, or connected to, your mobile phone?
Two spring to my mind immediately:

The Sipix A6 Infrared thermal printer. That printer is about the size of a paperback book, uses tiny sheets (or rolls) of thermal paper about half as long as standard paper. ("A6" paper for you office supply fans!) and connects to WinMo or Palm OS devices with a infrared port. It's hard not to feel like James Bond or Jack Bauer when someone sends you an important email, and you print it out right there on the dashboard of your car!
More often, of course, I'm printing a restaurant coupon, shopping list, or recipe, rather than an important email from the President or MI6, so, sadly, I typically feel more like Martha Stewart than James Bond.

A solar charger with USB outlet.
Imagine your plane goes down, stranding you on a remote island inhabited by polar bears, monsters, and a weird group of people creating a new society. Oh, sorry, that's the plot of ABC's "Lost." In my case, this solar charger with 2600mAH lithium ion battery serves two functions- a backup power source for travel and camping, but more often I use it for MP3 playback in the car from my phone. My RF modulator picks up interference from my cell phone charger, creating a faint whine in the background of my music. Unplugging the charger to silence the whine means that bopping to embarrassing 80's technopop ("We can dance if we want to, we can leave your friends behind...") runs down the phone battery unnecessarily. Using the solar charger, which isn't connected to the car's electrical system, eliminates the interference, and keeps the battery topped up.
I still take in on plane flights, though. You never know....
So Connection- I'll bet you guys and gals can top this- give us your weirdest accessory, or the weirdest customer request for an accessory that you've been asked for, even if it doesn't exist.