Usually it’s something to write with. Pen, pencil, highlighter. No clicking, just flicking them back and forth, forever. But if I wear a long enough necklace, I’ll play with that instead or too.
Highlighter, pen or bulldog clip. I slowly destroy everything on my desk.
Did you know you can take out the wire parts of a binder clip? I’m sure you did.
But did you know if you put the legs of one wire in the head of the other, then press down on it correctly on a desk, the “head” wire flies out?
What’s that I hear? The sound of 60,000 tongues being bitten simultaneously? Too easy. too easy, leave it alone…
AARRGGHH!
How YOU doin?
I coudn’t resist. 
I have several stress ball giveaways on my desk, but I don’t use them. The foam doesn’t last if you use it. Mine are just decoration. Instead I have a paperweight. We have unique ones here. They are all handmade. Take two pieces of very thick, supple leather and cut into circles about six inches in diameter. Sew along the edge. Fill with birdshot, then complete the sewing. Each weighs about two-three pounds.
Great exercise for hands, wrist and arms. I use one to relieve stress by squeezing it and banging on the desk. If I were to slap you upside the head with it, it would [del]probably[/del] definitely crack your skull.
Why do we have them? We have plotters so many of our documents are quite large, as in three feet by five feet, and larger. Just walking by a pile of these generate just enough of a breeze to make them hover off of the tables. The paperweights prevent that from occurring.
I never could wear non-metal watch bands because I would fidget them to death. I’ve mostly mastered my fidgeting now though. I still fidget with my Tivo remote control though; press play when the program is already playing, slide the keyboard open and shut.
Rubber finger page turner thingies. I stick one on in the morning pretty much as soon as I sit down at my desk and it stays on most of the day and I fiddle with it constantly. Under my desk is a rubber finger page turner graveyard because they eventually get away from me and invariably roll away under my desk.
:o yeah I know, the door was opened way too wide, I thought about it afterwards… hoping as usual my post would go unnoticed!
Gah! Everything already listed and more. In meetings at work I play with my badge, in the car I click the button on the gear shift constantly, at home watching television it’s usually a beagle’s ear.
Since nobody has gone the TMI route I geuss I will:
I’m constantly picking at the hair or stubble growing out of my damn ears!
No matter how hard I try, I always miss at least one when I trim them. This promts me to fecklessly pluck the offending hair out.
I do much the same as the OP. Tear labels off of bottles. Tear paper up, rip patterns into notes, click pens, mess with mechanical pencils. It’s bad!
It’s alliiiive!
I thought about this thread while playing with a holiday gifts. If you’re a fidgety person like me, check out these things.
Now, what I have is a Chinese knockoff (which I will not link to) because these aren’t yet available to non-bakers, but holy shit. This cube is an extraordinarily satisfying toy.
Plus one. My wife gave me a fidget cube for Christmas and I love it. I often use it in my office when no one is there.
I have a Tangle at my desk, and I love it. I just noticed that they have a “hairy” one, so I’m off to buy that. 
This. Either my own or my husband’s or both.
That must get awkward at work.
I tear up styro cups into tiny pieces, fold paper or do math puzzles I can make up. What ever I can get my hands on seems to work. This morning while working the coffee bar I was seeing how straight I coud get paper clips.
It’s a bit situational, but I have a chromed brass thumb rest on each of my bass guitars that I really like to stroke between songs while not actually playing the instrument.
Thumb rests on basses are a throwback to the 60s and 70s, and the cool kids don’t use them anymore, preferring to rest their thumb on a pickup or on one of the strings. But I love them. It gives me something to … caress… Smooth and cool. Like a Native American worry stone. I imagine that in a year or two I’ll wear through the chrome plating and the brass will show through.
There are many places to attach one, but my preference is as shown on this guitar.
I’m not a fiidgeter but I used to have a large stainless steel, screw and bolt. It was kinda heavy and big, but it was awesomely tooled. I carried in around for several weeks during an attempt to quit smoking. People did find it a little odd, but also insisted on holding it, trying it, grooving on it. I wonder where that thing went?
I often carry stones around in my pockets, smooth, sometimes shiny, always a pleasant weight, size, shape. (I also sometimes come home with a rock, when I walk my dog.)
Lately it’s been a rose quartz polished heart, about the size of a very large grape, but heavier, of course. It’s always in my pocket theses days! I had a moonstone one for ages, but I misplaced it eventually.
I have a couple different sizes of Eggsercizer like objects that work well for me.