Headhunter, Shadows and Dust gloves and ?

Headhunter gives modes while Shadow and Dust gives fun by counting killed mobs + damage after some meta is reached.

Are there any other items that gives fun/more content to exile or to the game? Because those two items together makes game very enjoyable and 3rd item with more/another game mechanic would be great :).

There are some other items that grant the same effect of the Shadows and Dust gloves.

There's also the Inspired Learning jewel that's like a partial Headhunter belt.

Some items like the Innsbury Edge also carry a hidden 'Insanity' effect that can trigger as you're playing.

Rigwald's Crest and The Scourge can summon Spectral Wolves when you get a kill.

I'm sure there are other items that have added effects

Sound effects:
The Whispering Ice makes noises when killing rare enemies Jack, the Axe and The Goddess Unleashed talk to your character
Visual effects (only a few):
Maligaro's Restraint, Singularity and Belt of the Deceiver give you a unique optic effect when equipped
The Aylardex changes the color of your power charges to purple
Unique skills:
The Dancing Dervish, The Whispering Ice, Star of Wraeclast and Blood of Corruption each grant a unique skill.
*Interesting* gameplay related effects:
Soulthirst grant soul eater during flask effect
Shaper's Seed and Kingmaker cause you to emit a unique aura
Death's Oath, Eclipse Solaris and Singularity each affect nearby enemies
Empire's Grasp reverses knockback direction
Those are pretty much the most interesting ones I found, I hope I was able to help!

Sire of Shards makes every projectile spell awesome. And even some projectile attacks too, or not-obviously-projectile spells, such as summon spectres, skeleton mages etc...