After the corkscrew, the foil cutter gets the most use in this house. This is a great little gadget and even cuts the top off screwcaps.
The Vac-U-vin corks are good gadgets, not that we use the Vac-U-Vin pump anymore as I don't think it makes any difference, but the corks can be used in place of the new-fangled DIAMS, which do a very good job of sealing the bottle, inhibiting oxidation and TCA, but it's so hard to get them back in again once they have been taken out. I have also saved a couple of Zork corks for this usage.
Someone here in NZ invented the ChampEazy, which was a gadget to open bottles of Bubbly. It's a bit of a nuisance to use for just one, but if you were in a situation where you needed to open several at a time, I think it would work well.
Dropstops get used from time to time as well. These are little circular pieces of flexible foil-like Mylar that you can insert into the top of a bottle to stop drips. Good for wine tastings where you have to pour about to 20 samples from the one bottle.
The three pronged cork retriever is one of those gadgets you really do need to have in the gadget drawer, for those rare but very annoying times when the cork goes in instead of out.
Oh, the other gadget I really like is a little 'hat' thingy that is used to reseal a bottle of bubbles. I've one that works really well.
Cheers,
Sue