My favorite corkscrew, hereafter known as Corkscrew A.
Every once in a while, you come across a device that is sublime in form and function.  While I can’t say definitively that this is the best corkscrew in the world, I can say that it is indeed my favorite corkscrew.  
I like gadgety stuff, but I need to weigh gadgety vs kludgey. 
What makes this corkscrew so good?  It’s subtle.
A lesser corkscrew, Corkscrew B.
Teflon coated screw for easy entry into the cork. Finger grips on the left just feel good in the hand.  The part where you rest against the bottle’s mouth to open?  There’s actually TWO ridges.  The style of sommelier’s style corkscrew (Corkscrew B) that I usually come across usually only has ONE ridge, making it difficult to leverage the cork out of the bottle once the corkscrew is in place.  Additionally, those two ridges have a small pin, so that when the closer ridge is being used, the farther ridge can be moved out of the way as necessary.
Corkscrew A has a form factor that when it’s completely closed, it’s still very easy to open bottles, without the added bulk of a large mouth.  Call it a personal preference, but I find that Corkscrew A sits in the pocket much better than Corkscrew B.
Caw caw! I have wings!
“But Russ? What about those neat wing style corkscrews?  What about them indeed?  What I find is that they’re intuitive to use, but very difficult to store and keep handy.  Honestly though, sometimes I find them a little awkward in the actual operation since it feels like you need three hands to secure it on the bottle and turn the corkscrew into the cork.  Sure they’re neat for what they do and people like to paint the arms in neat ways or make them into robot arms, but for my tastes, it takes up a lot of space for something that Corkscrew A does in a smaller space.

Finally, there’s the cost.  It’s a simple device, it’s elegant in operation, and it’s cheap.  Under 10 bucks.  More complicated style wine openers can cost upwards of 40 bucks or more and not work nearly as well.

The only thing I can think of at the moment to improve on the design would be to put a guide ridge where I could rest the top of the bottle so that the knife cut at a uniform height on the foil.

But that really is a minor gripe considering how well this tool functions.