What are all the different ways that LEGO pieces join together?
Currently in use:


Stud and "antistud" (diameter 4.6mm)
Longer studs (Minifig torso)
Minifig legs
Minifig neck and head / accessory (eg backpack) - also compatible with studs
Clip and bar (in a way, similar to stud, but with diameter 3.2mm)
Wheels (3.2mm axles)
Flower connector (similar, but even smaller, present in a surprising number of parts, including spider and Technic chain link)
Technic hole and pin (compatible with studs)
Technic axle and axle hole
Turntable
Click hinges
Ball joint sockets
Brick hinges (I'd wager this one is the next one to disappear)
9v/RC track connection
PF electrical plug
NXT electrical plug
Train magnets, embedded
Pneumatic hoses to pneumatic elements and bar elements
Sliding door in grooves
Visors on helmets


Decommissioned:


Flat hinges
12v track clip
4.5V/12v electrical plugs
9V electrical plugs
Train magnets, free (connects to flowers too...)
Tube plate hinge (with red tube)
Wheels (metal pin, as in blue era train wheels)
Wheels (Plastic pin, as in grey era train wheels)
ZNAP
Homemaker arm joints