Ninja Pajamas, and other good things.

Fresh Meat - Tower Blaster
You and your clean-shaven aryan eunich followers are in an intellectual battle against red-headed bastard vikings. Okay, that's reading into it a bit. This Towers of Hanoi-reminiscent puzzle is turn-based and increases in difficulty on each level. Your little midget people boost your self esteem by cheering your every move for added excitement. Because it has no time limit for moves, you can easily play it during a boring conference call.

Ease for the uncoordinated: 5/5 - no time limit
Simplicity: 5/5
Strategy Factor: 3/5 - because you can figure out what the other guy has if you watch and write it down.
Ease of beating Ayric: 5/5 - I know this instinctively
Addiction factor: 10+ games in a row. Reheats well.

Old Game - Blix
At one point, I was the BlixVixen. I can play this game for hours. It's got candy-colored Fifties-style goodness, with a funky disco space monkey theme and techno music. It increases in difficulty very slowly, and with a password (and cute little quickie flick) every five levels, you don't have to start all over again when the Blix bug revisits you, yet unlike most flash games, there are (I think) 200 levels or so for free, and another 100 for subscribers. Not only that, but you can watch the Blix single on Atom Films (B-).

Ease for the uncoordinated: 3/5 - mouse only, but some quick clicking required.
Simplicity: 4/5
Strategy Factor: 3/5 - most have a pattern that you can figure out to advance.
Ease of beating Ayric: 2.5/5 - He was really good, but he bores more easily than I do, so I've gotten farther, but more through perserverance than skill.
Addiction factor: Not enough data to calculate. I started playing this game in late 2000 and I still like it. Infinite shelf life.