Huge board game fan, gamer, and designer (currently working on a "United Nations"-themed global warfare game). I've played all the iterations of Axis & Allies, but own the Wizards of the Coast 1942 (2nd edition), which is probably the most "adult" and "balanced" version. Played a bunch of Settlers of Cataan too, also Pandemic. Check out
http://boardgamegeek.com/Without getting into a specific board game, here are some things I don't like that piss me off:
1. Your fate is determined on the first turn. Be that in the form of a dice roll or whatever, a lot of strategy board games give you an initial position advantage based entirely on a luck mechanic.
2. No opportunities for rapid comebacks. I'm all in favor of two or three players dominating a game, but if the underdog is left behind after the first few turns and there's really nothing pragmatically he can do to win... that's a little upsetting.
3. One easy path to victory. Sure, most games revolve around sum total points or whatever, but if there is game that involves a singular method of winning without leaving room for experimentation, then that game has problems. Similarly, if you wind up doing the same thing every game, that can get old.
That being said, I can't tell you how many times I've played Settlers of Cataan, and either the owner of the game or whoever got to go first won. I've stopped playing it as a result.
Axis & Allies on the other hand may come across as linear since there is a lot of setup prior to the game (each nation starts with certain #s of units in various locations). This sort of makes A&A more like a chess game, in that you're limited to what your pieces can do at certain times... however there is a lot of room for experimentation. Historically correct military operations tend to work in your favor (go figure), but there are plenty of options you can take if you want to go outside the history book (i.e. what if the US began arming the Republic of China instead of tacitly supporting them?) which is what I like about the game. You will also have a different gaming experience depending on which country you play as, which is also cool. It's a hard game to learn, but once you know the rules intuitively it can really speed the game up and make it fun.
Pandemic is a really fun and easy co-operative game. The game is very organic, in that the luck/chance mechanic can go one way or another. Different game every time you play it. It's also easy to learn and play, so if you're more into casual gaming when hosting dinner parties or something, it can be fun.
Merchants and Marauders, Le Havre, and Lords of Waterdeep have simple mechanics and are fun.
That's all I've been playing lately. One other thing worth mentioning is that if you can play a 4-7 player game by yourself and find relative enjoyment out of it, then more people will make it more fun. That's my litmus test.
