Six favourites:
Favourite multi-player: Dune by Eberle, Kittredge and Olotka / Avalon Hill. Still the greatest for me. The perfect blend of strategy and player interaction. The theme vividly evokes the books. The opportunity for clever play abounds. Let down by rules that are vague on key points.
Favourite wargame: Rommel in the Desert by Besinque / Columbia Games. Manages to fit great strategy into a game that has < 20 pieces in some scenarios. Revolutionary in many ways: really captures tempo as the essence of warfare. The month-end refit rules are a let down.
Crazy Fun: Diceland Space by Goettsch & Ernest / CheapAss. Throw giant paper dice, each representing a space combat ship, in an attempt to knock over / trap / or line up a shot on your opponent's ships. There's strategy, there's throwing skill and there is plain chutzpah! Downsides are it is hard to store and no-one takes it seriously enough.
Favourite Communication Game: Barbarossa by Teuber / ASS. Set your own riddles in clay. I love the creativity here of setting a challenge that is intriguing enough to attract attempts, but not so easy it is guessed straight away. Some of my favourite sculptures (by friends - as modesty requires

are "evolution", "gravity" and "croque en bouche"... Downsides are not being able to spell "croque en bouche"
Favourite Euro: Tigris & Euphrates by Knizia / Hans im Gluck. This game is superb: it packs so much thought and fun into a relatively short and great looking package. I love the way the board is so dynamic where terrible catastrophes can completely obliterate empires that once threatened to rule the known world. The luck here doesn't worry me: it adds to the drama.
Favourite Game I wish I played more & better: Go or Wei Chi. This is a game that has an elemental quality. In the same way that Newtown and Keppler inferred the laws of gravity, the originators of this game must have discovered it more than invented it. It has a beautiful early phase with a very intuitive quality to the play which then gets resolved by a lot of down and dirty knife fights. Downsides: awakens a certain desire for a beautiful board and stones that the wallet and frequency of play can't satisfy.