Stone Age
by Rio Grande 2-4 players
Is a four player game that sort of reminds me of Puerto Rico's game mechanics. Basically you have villagers that you send out to work and build resources. Each turn a different player goes first and you have to decide on several different Strategies for building your civilization/village.
For example each turn you can choose from gathering one of four different resources, hunting for food (you have to feed your villagers), building tools to help gather resources, increasing your agricultural capability (so you don't have to send out so many hunters), buying technologies, building huts
..etc
It is really difficult to tell who is winning until the end of the game, but the whole family (including the wife really enjoys it). The game components are pretty high quality with thick card stock and wooden playing pieces.
Quick to learn, but it is best learned by actually playing. Luck in the die roles for resources, but as far as strategy goes you have a lot of options!
Alhambra
by Queen Games 2-6 players
This one is similar in the puzzle building aspects to Carcassonne, but with a slight twist. You have to choose each turn between buying puzzle pieces and collecting money. If you can pay exactly the right amount then you can do a second action. Each person is working on their own garden, and there are three randomly occurring scoring rounds.
A fun family game and very quick to learn. Good re-play and it looks like there are a lot of expansions available.
Battue, Storm of the Horse Lords
By Red Juggernaut 2- 4 players
This is a fast play game where each person takes a hoard of barbarians and tries loots a city. The city is composed of randomly selected tiles that are placed face down. Each tile has a defense value, a loot value, and possible event cards. Rules are fast and easy. The players can attack each other through action cards or directly. They can also just ignore each other and focus their resources on getting the most loot. Played with 2 and 3 players so far (definitely more of a guy game than a family one) we liked it. You can play a couple of games in an hour. There is at least one expansion, and one planned (possible to make a 6 player game?).
Fun, fast, easy rules, Strategy limited with lots of luck involved.
Amuse Amaze
By HL Games 2-6 players
In this game you race your way through a maze by spelling words (Think Scrabble). You have some letters in your hand and you can pick up extras along the way, but you have to rely on the letter combinations on the various boards.
This one was a lot of fun for the whole family, rules are easy, and anyone who likes scrabble will enjoy this one as well. Also it was a bargain at $20. USD
In general I would recommend these for good game buys. Battue has a little more limited audience, but the rest are very good family games for almost any age (Stone Age is a little complicated for younger than 10 maybe).