Ok here are the ones that I am familiar with...

• First Person Shooter (FPS)
• Real Time Strategy (RTS)
• Sports
• Simulation (including Flight, Sim series)
• Racing
• Role Playing Game (RPG)
• Strategy
• Arcade
• Adventure

I know occasionally there are games that don't fall into one of these categories or fall into multiple categories but these don't define a new genre...
Have a missed any or are these all of them?

Some of these genres can bleed into other genres. Take for example Platform games; these games can be considered adventure games.

Platform....
That is one I didn't mention...

you cant put flight sim in another category, it is it's own category.

Sim city, sim planet

Silent serviceII

MS flight simmulator even deserves its own category. Boooooring.
give me an f16, yf23 and I will fly cross country but when I get board of flying I can go blow up a tree or fly mach2.5 at treetop level. Muhwahahahahahah.

But FPS is my world now.

never, never forget: Turn Based Strategy!
look at all those names!:
Heroes Of Might And Magic
Worms
Civilisation

for me, RPGs are divided into 2 groups: AD&D style and console style.

It is it's own category, flight simulation. It's easy to treat flight sims as a form of FPS air combat. Rather than learn the " boring" basics of piloting; flight path, instrumentation,vectors, etc.