Backgammon is a solid choice, always.

For me, it's Carcassonne. It's sneaky complex in as much as one can learn how to play in just a couple of minutes but in order to play well it takes strategy and calculation. It's great.

Risk

Supergang, some sort of gangster monopoly where bank robberies or opponent assassinations are resolved with a dart pistol.

Full Metal Planet, a scifi strategy game played without a dice.

I was also quite fond of Cry Havoc (classic hex wargame), the Fury of Dracula (some variation on the classic scotland yard), Armada (some new world plundering game), and also Junta (a backstabbing banana republic simulation) was quite fun. But my favorite were these two games above, by Ludodélire, the authors of Knightmare Chess...

Battleship.

7 Wonders!

It's Civilization meets Settlers of Catan. A brilliant game. Tons of fun.

http://boardgamegeek.com/boardgame/68448/7-wonders
http://www.amazon.com/Asmodee-SEV-EN01ASM-7-Wonders-Game/dp/B0043KJW5M
https://www.youtube.com/watch?v=Cjv1JfFeQko&feature=plcp

Hmm, sort of like that enigmatic title you've given yourself.

EDIT: As for the game, I used to love Michigan Rummy ans Sequence.

My favorite is Chess. :-)

There was another one I used to play, kinda like Making History except as a board game, but I can't remember the name of it. It was pretty fun though

MONOPOLY!!!!

Chess.

Chinese Checkers.

Monopoly.

There are a lot that I love, but here are a few that I'm particularly fond of:

Fury of Dracula: sort of like Scotland Yard, but with more Dracula! Best mix of gameplay and theme that I've yet come across.

Arkham Horror: great for when I don't have time organize a campaign of Call of Cthulhu RPG, but want to get my Lovecraft fix in.

Battlestations: If you enjoyed FTL, this is pretty much the board game version of it. But with /tons/ more items and crew customization options. Including laser monocles!

Duel of Ages: You've seen that flash video, "The Ultimate Showdown of Ultimate Destiny"? Imagine that as a tactical boardgame. If you've ever wanted to see Beowulf riding a bicycle across the surface of Mars so that he can fire a rocket launcher at The Predator, while in the distance an angry unicorn battles space bureaucrats and their pet velociraptor, then this is a game for you.

Cosmic encounter: love this game. The basic concept is fairly simple, but the massive library of unique alien powers turns every single game into chaos, betrayal and madness.

High Frontier: A highly detailed simulation of planning near-future space missions within the solar system and industrializing asteroids and moons. The amount of scientific research that went into this game is staggering. I'll admit it melts my brain a bit, but I'm still in awe of it. Space program geeks should definitely check it out.

The Hellgame: Without question the most evil, backstabby, treacherous game I have ever played. Don't play this with bad sports, or your friendship will be over.

Go: The only boardgame that's ever helped me to understand an entire system of philosophy (Taoism).

Puerto Rico: a big nostalgia item for me, since it was the first board game to show me that there was a whole world of complexity beyond games like 'monopoly' and 'clue'.

- Betrayal at the House on the Hill
- Mare Nostrum
- RoboRally
- Junta
- Go

Definitely Arkham Horror. Then chess. Also, while this next game is really simple and probably nothing that could be considered anything special, I really enjoy The Mysteries of Peking as well. These are my top three. Also, while technically a card game, Bohnanza is really good.

Board Games
- RoboRally
- 1835
- Hero Quest

Card/Dice Games
- Doppelkopf
- Yatzee
- DiceRPG