I was sitting and watching my cat face off against one of his many foes, the bathroom door, when it occurred to me that a cool game could be made from playing a cat. You've got your platforming elements, as you try to leap from floor to countertop to refrigerator to top of the cupboards, you've got your hunting and combat elements, obviously, and you have your boss battles against the ents (humans) roaming your domain.

Then I remembered...it's been done:
http://en.wikipedia.org/wiki/Alley_Cat_(game)

I'd like to see a game that has satellite elements that can be played on portable devices.

Sega attempted this with Sonic for the Dreamcast, which gave you little tamagotchi like things that you played on the portable memory unit.

The newest version of Outrun lets you port your game progress between the PS2 and the PSP editions.

I'm thinking of something like the former, where, say you have a racing game, and you earn enough cash to upgrade your transmission, which gives you a +3.5 in gear shifting speed during a race. Now maybe you cane take your save game on a memory card, plug it into your palm pilot or pocket pc, and play a puzzle game as your mechanic, which will give you a +4.0 if you win.

Maybe an adventure/mystery game will pop up text messages or emails with clues, or give you small little paper puzzles to decrypt things like passwords, in the guise of a 'password cracking' utility, or somesuch.

Maybe I've just been missing it, but is there a billiards game that offers a large variety of games?

See the wikipedia entry for billiards:
http://en.wikipedia.org/wiki/Billiards

And you see that while there aren't quite as many variations as there are with cards, it's still a respectable number, and I can see Snooker being a popular third after 8 ball and 9 ball.

The first link that comes up in Google for 'snooker pc' is this:
http://www.gamespot.com/pc/sports/virtualsnooker/
from 1996!

Seems to me there may be interest in a "Hoyle" like billiards compendium.

These aren't games that I'd necessarily buy, and in some cases, there're pretty sound fiscal reasons why these games don't yet exist. It's just that I find their absence curious. I mean, I can't be the only person who's thought of these:

Harlem Globetrotters
Now this may work better as an unlockable mode in the NBA series, ie unlock a new Globetrotter with every championship, and when you've unlocked enough Globetrotters to make a team, you can play exhibition games in Globetrotter mode.
Or maybe there's a decent standalone game to be found there.

Stickball
Why doesn't this exist? In fact, why doesn't Spalding license/advergame a whole suite of pink ball/"spaldeen" games, stickball, stoop ball, handball, etc. Here's the rules:
http://www.spaldeen.com/gamesrules.html

College/Olympic wrestling

Kickball
And dodgeball, for that matter.