I've seen a few, more often when I'm caddying for someone. I'll list what I can from memory:
On the first hole, a shorter par four with trees right (the safe play is left, but if you go right you can have a pitch shot for your approach), a competitor says "Boy, look at those trees on the right. Did they take some out in the past few years?" in an obvious attempt to get everyone thinking about the trees on the right.
One girl would routinely wait and delay and never take the honor even if it was hers, and would say "go ahead if you're ready." This is borderline not "gamesmanship" and outright cheating, though.
Someone said to another (I was in the group but it wasn't my player) "Man, you could be pretty good if you could only putt." The person was a perfectly good putter, but you could see it affected them.
Standing a bit too close to someone is common. Just out of the really near field, and not exactly staying super still.
The age old stuff - "do you breathe in or out…" stuff doesn't get used too often, but you'll still hear it occasionally.
The really old stuff - conceding a bunch of early putts and not doing it late - often hurts the gamer more than the gamee.
I've seen people suggest "you should hit a provisional" when they know darn well the ball is fine. It throws the person off sometimes. One guy told me he loved to do that on holes where you couldn't see the landing area very well.
My personal favorite!
No in all honesty I feel the same way @iacas feels, they are purely functional until they are so gross that they must be tossed. Working at a golf course for all these years has ruined me from buying hats when I play different courses. I know how much those hats really cost wholesale, and I have a hard time paying $35-$40 for a $13 hat, I don't care if it does say Pinehurst no 2 on it.