Nicely done, Hal.
I went with the tail because I lack imagination. Upon reading through the thread, I think gills would be pretty cool as well. Eyes on stalks is just asking for trouble–I’d squash mine in the car door or get one mangled in an engine somehow.
Nobody wants to get with the guy in the club with strange eyeball stalks. A tail, though, is a perfect conversation starter.
Tail. 'Cause I haven’t had any tail in a while.
Flying squirrel glider flaps.
If that’s not feasible, then cat/fox ears, swivel and independent motion included.
If that’s not feasible, then a prehensile tail. (a nice soft fuzzy one - no ratty tails, please.)
I’m almost alone in my eyeballs on stalks love? Sigh. You guys have come up with some great other ideas, though - amphibious gills would rock my world. I would also like the glider arms. I think the dog nose would be too much - it would be hard to live in our world being able to smell that much.
tail. you could goose people next to you and get away with it.
You can have 'em, but they won’t be of much use for gliding. People who wear wingsuits (which are basically strap-on flying-squirrel glider flaps) still zip along through the air at around 80 MPH, which makes landing without a parachute problematic.
If that’s not feasible, then cat/fox ears, swivel and independent motion included.
Your high-sensitivity independent-swivel ear cones sound cool.
What I want are ears that I can close myself. This would be extremely useful around loud noises and while swimming or bathing. It would also make sure I don’t stand out as a freak in a crowd.
I guess if you had a prehensile tail, you could always tuck it in if you didn’t want to look like a freak. It would be a waste of a prehensile tail though. 
It might give you a distinct advantage though, I recall reading about how much a dog can supposedly tell about a person just by sniffing them.
As for looking like a freak I was kind of imagining this scenario is taking place in a reality where such body modifications are commonplace. I actually had a rather heated online argument elsewhere which was inspired by this thread. I’m all for it, others not so much.
swish swish swish
That is indeed what I was thinking - a Body Mod Shoppe in every neighbourhood like we have tattoo shops now.
I was discussing the concept of cheap and easy body modification in a chat room earlier, I was amazed at the tidal wave of apocalyptic fury that descended upon me, about 1/3 of the people there were for it and 2/3 against. It seemed to be mostly based on the premise that we should learn to love ourselves internally and externally rather than modifying our appearance and that if it became available everyone would end up looking the same.
And that I was a beast, a beast for suggesting otherwise.
To which I say, “Bollocks to that”
chases tail, falls over
I’d rather have two extra arms. It’d make it easier to lift and sort things. Plus, I could work at a freak show for extra cash.
Trying to buy shirts would be kind of a drag, tho’.
80s style wife beater or t-shirt with the sides cut open. Unless your wish for extra arms gets a particularly evil genie, and he gives you arms on your ass or something.
I’d go with the tail over the eyestalks, no question. And not to worry, tail fans, a solution to the pants problem has already been found.
applauds
I might consider a 3-armed configuration, like the aliens in The Mote In God’s Eye. On the other hand…
That seems unlikely, if everyone can modify their body any way they feel like it. Or maybe they mean everyone is going to end up with wings, gills, four arms, four legs, a dog nose, fox ears, eyeballs on stalks, and a prehensile tail. That also seems unlikely. 
Straight Dope Ignorance Fighting Time, or: The SDMB word-a-day machine!
It’s called a patagium.
If you watch some old Rocky and Bullwinkle cartoons, you may note that Rocky is drawn Anatomically Correctly. He has a patagium, which is visible in some of his flying scenes.
I’m all about the wings, personally. Being able to fly under my own power would be super nifty!
Having heard the unparalleled excellence of eyeballs on stalks from my better half over the years, I can appreciate their advantages as well. Trying to see over or around something? Done. Trying to see behind you? Done. Actually a pretty good tool, I’d say.
I voted “Prehensile Tail”…
…but in my head, I’ll think of it as “Second Penis I Can Also Pick stuff Up With!”