Links for the H.M. in the database
Arimma: http://boardgamegeek.com/game/4616
Abalone: http://boardgamegeek.com/game/526
Akron: http://boardgamegeek.com/game/10889
Accasta: http://boardgamegeek.com/game/9060
Anchor: http://boardgamegeek.com/game/23235

I agree with your choice of Amazons, but a relatively new "A" abstract that I like a lot is Abande by Dieter Stein

http://www.boardgamegeek.com/game/21324

You can play this at www.superdupergames.org

Sorry, i simply have to vote for Abalone for the "A".

Amazons gets my vote too. Honorable mention to Avalam Bitaka http://www.boardgamegeek.com/game/9092

my vote goes to abalone as well

Abalone is interesting for new players, but not very deep. The traditional initial setup is seriously broken: I have yet to find a player or AI that can beat me with that setup. (I have found people who understand the same thing I do, and those games always end a tie). I ended up "state champion" by doing nothing but pulling the cheese tactic off over and over again.

The scattered setup is more interesting, but really doesn't feel like abalone anymore. Because of that, I wouldn't really say it would qualify as "best". Amazons on the other hand is very interesting and deep.

I would like to add as an honorable mention AXIOM : very original, interesting and fun !

I also agree that Amazon gets the vote instead of Abalone, for all of the reasons mentioned above. Good work.

What about Blokus?

Links for the H.M. in the database
Breakthrough: http://boardgamegeek.com/game/3825
Byte: http://boardgamegeek.com/game/19360

This is a tougher call. I think I would have given the nod to Blokus. But I also would have given Blam! an honorable mention.

Blokus http://www.boardgamegeek.com/game/2453
Blam! http://www.boardgamegeek.com/game/17765

I understand those who want to mention Blokus. Personally, I find that it lacks clarity in depth, like most -omino games. To me, it plays like a sequence of depth-1 best guesses, with very little ability to see several moves deep. Admittedly, this might just be my experience and not intrinsic to the game.

I have to respectfully disagree with you there. I find myself always looking at least several moves ahead when considering my current move. Since each of the 21 pieces is unique, it's an imperative to know where you are going and what pieces you'll need to get there. Often, it's a matter of laying pieces between those of two other players in such a way as to break into their 'backfield.' And those offensive laydowns will have to be weighed against your defensive requirements in stopping the other players. Determining which pieces are gobnig to be used offensively and defensively is crucial as the game develops.

What I found so surprising about Blokus was that it was considerably deeper than I had expected after reading the rule.