Most of the good board games come from Germany, though I don't think Carcasonne does.

Some of my favourites:

Settlers of Catan (aka Die Siedler von Catan) - 2 to 4 players (2 to 6 with expansion) - simple rules, roll dice to see which hexagonal tiles produce goods, then trade with other players and spend them to get more roads, towns, cities and VPs. Bad luck can be frustrating.

Puerto Rico - 3 to 5 players - every round, each player takes a job so everyone can buy a building or build a plantation or ship goods etc. Not all jobs are executed in a round. Game strategy is juggling between increasing productivity, acquiring cash and competing for limited shipping space and predicting and adapting to the strategies of other players.

Ursuppe - 2 to 6 players - a bizarre game of tribes of amoeba eating different types of food in a primordial soup and acquiring gene cards in the competition for that food. Gene cards include better movement and eating other amoebas.