I can give cats injections (assuming the stupid cat hasn’t hidden herself away under the bed).
I can extract hummingbirds (and other birds) from mist-nets.
I can sleep pretty much any time I try to.
And I can yell very loud.
But not both at the same time.
Is that steam extraction, or do you use methylene chloride or something? And who uses hummingbird extract anyway? 
I can peel an orange leaving hardly any of that white stuff.
I can catch chipmunks using nothing but a plastic trash can and a tennis racket.
I can keep my head when all about me
Are losing theirs and blaming it on me
Like this?
I can usually make a yummy dinner out of whatever weird things I find in the fridge.
I can recite all fifty states, in alphabetical order, in under thirty seconds. I also, like DavidwithanR mentioned, can sleep pretty much any time I want to.
I can be a real bitch when I need to be.
Well, I meant to put a string of smilies here but it’s not working.
I can find stuff my Wife has misplaced.
Once, she lost her phone. It was not on so we could not just call it and search for the ring. I determined that she had used it in her car, and may have dropped it in the drive in the snow when she got home.
I had since plowed the driveway.
I determined where it would be in the plowed snow piles if she had indeed dropped it. I found it in about 5 minutes (intact). I’m very good at retracing a persons tracks and what they may have done. I’m sort of like Monk when it comes to that. Comes in handy.
Thread winner. Amazing.
For me, I can make anyone avert their eyes, instantly. Instantly! Anyone! 
I like to have my chosen humans around me, but if they aren’t available I can be alone with no detrimental effects, for extended periods.
I can swear like a Cornish fishwife in Esperanto. 
I can scrutineer ballroom dance competitions (by hand), usually fast enough to keep up with an ongoing competition. (I start falling behind at around 7 or 9 judges, which is more than anyone ever uses.)
This isn’t too rare or unusual, but I can play a lot of music by ear, often lengthy segments of music or entire pieces without ever having seen the music sheet/score once.
I can also recall extremely intricate sports stats or military trivia facts.
I can also draw fairly detailed maps of some world regions by memory.
I’m the same way but with horsepower and torque numbers on sports cars. And their lateral g capabilities.
Sorry about the length, but I rarely get to brag about this, since I work in a cubicle now. I have unusually good spatial awareness skills (this runs in the family, btw).
The following are things I’ve done as a job:
-I can reverse (back in) tractor trailers and other trucks with uncanny accuracy. One job involved taking trucks from their drivers (they weren’t allowed to park them) and packing them 20 at a time so close you could not walk between them.
-I can sort and shoehorn lots of airplanes into a hangar with a tug. I “memorize” the shape and size of the space and push the plane into it without needing to check again. It’s kind of like a giant puzzle. I did this on a night shift by myself (no observers) for over a year.
-I can operate a large crane (35 ton) on a floating vessel, and place loads on other vessels (also bobbing on the waves) with uncanny accuracy. I’ve even placed loads on vessels while underway (moving past us, it was necessary in a few odd situations). I also operated a crane holding equipment for divers 5-600 feet below. I had to position the loads watching a closed circuit camera and compensate for waves as the divers worked.
-I “drove” a large semi-submersible vessel for a few years (it crawled along the seabed using a spiderweb of cables anchored to the seafloor). I occasionally had to snuggle up close to oil rigs without bumping them. I would frequently get calls from the divers to “move starboard 8 inches”. The vessel was 650 feet long and 45,000 tons, so accurate placement was very difficult.
-I’ve mentioned here before, I’m a licensed commercial pilot and flight instructor, and although not as difficult as the items above, this does require some spatial skills.
Non-work:
-I can tow double-trailer setups and back the entire thing into any spot you choose (truck, camper and boat). I’ve had many combinations of these and have done this for years on family trips. These are ~70 foot long, 12-wheeled rigs, not something small.
If I haven’t bored you yet, I lack a normal spatial skill most people have. I cannot catch/throw balls with any accuracy at all. I’m noticeably bad at this.