sf asked and others answered:

quiche
custard
meringue
sauce
fried
boiled
poached
deviled
in sandwiches
Egg Nog
Raw (power drink)
Egg Salad
Decorations (hollow out egg shell)
Mayo
cakes
coddled
Omeletized
As a binder. Meatloaf and turkey dressing comes to mind
scrambled
pavlova
angel food
7 minute frosting
marshmallows
tapioca
salad: both hard boiled, sliced in salad, and egg salad
in potato salad
in baked goods: cakes, cookies, etc
at this cafe near us: over-medium on top of a burger
benedict
Egg foo young
baked eggs with nettles in Madrid
egg drop soup

Each pleat in a chef's toque allegedly represents a different way the chef
is supposed to know how to cook eggs. To the items listed above I'll add:

truffled
eggs Sardou
eggs Florentine
curried
baked with cream
stracciatella
in fried rice
as the sauce in spaghetti carbonara
in ice cream
brushed onto the outside of a chicken as it spins on a rotisserie
soufflés

There are two good ways to scramble eggs: One with slow heat and constant
stirring to end up with a custardy outcome, the other with high heat and
rapid stirring to end up with billowy soft curds.

There are plenty of ways to fry unbroken-yolk eggs, too: Over-easy,
over-medium, over-hard, sunny-side up, with the lid on the pan to
approximate over-medium, with the lid on the pan and some liquid added so
that the egg steams while it fries, in a ring so that you can make an
English-muffin sandwich, basted with bacon fat, or in a half-inch or so of
olive oil (with smoked paprika and garlic on top).

I'll bet my Gourmet cookbook has more ways than what I've listed, but I
think that'll do for now.

Bob