So there you are, in the Target game aisle, and you see one of those games you’ve heard about from friends: Settlers of Catan. It comes in a sturdy-looking box that’s taller and has a smaller footprint than your Monopoly board, and when you pick it up for a closer look you realize it’s a forty dollar game. What gives? Who pays that much for games? Or maybe you’ve heard some tantalizing line about how we’re living in the golden age of great board games, or you’ve taken a peek at a friend’s game shelf and seen boxes with names like Carcassonne and Agricola, but you have no idea where to start.
You’ll sometimes hear this style of game referred to as a German-Style board game or a Euro Board Game. There are some consistent characteristics: They emphasize strategy. They may take a while to play (probably more than a game of Clue, but much less than a game of Monopoly). They’re unlikely to involve player elimination, and although there’s generally a randomizer element like periodic dice rolls, they’re much heavier on strategy than luck. They also tend to cost more, and come with higher-quality components. (I remember once taping a Hi Ho Cherry-O box back together for the third time, wondering how much they would need to charge just to give us a box that wouldn’t fall apart in a month.)
If you’re ready to take the plunge, one inexpensive game you might consider starting with is Forbidden Island,
This is a game with a cooperative rather than a competitive mechanic: the whole group works together to gather artifacts before an island is covered in rising waters, and either you all succeed, or you all fail. Forbidden Island has beautifully illustrated cards, wood player tokens, and sturdy plastic sculptures to represent each artifact. It’s marketed to families but can be enjoyed by adults, and it’s actually a very similar mechanic to the game Pandemic, where players work as a team to stop an expanding global plague.
There are also some terrific games you’ll find in game stores that are less strategy-oriented and would be better described as smart party games. Dixit 
If you want a chance to try before you buy, seek out friends who hold game parties, or a Board Gaming Meetup. A lot of these games are better with more people. Searching for “board game meetup your_town_here” is a good place to start, but also, if there’s a game specialty store near you, you could call up and ask. They may also have open gaming nights. If you don’t think you have a game specialty store, try asking the comics store (there’s a lot of overlap).
Game specialty stores will have an enormous range of games, from cheap to expensive and from simple to incredibly complex. Staff at these stores are often pretty knowledgeable and can recommend new games based on what you’ve enjoyed in the past or what you loved as a kid. If your game shopping experience has been entirely the game aisle at Target, you should check out a game store just for the fun of browsing.
Another excellent source for knowledgeable advice is BoardGameGeek. It’s full of reviews, conversations, suggested rule hacks (Monopoly variant: bankrupt players become ghosts that haunt hotels and houses on the board) and much more. If you want to know how long a game really takes to play, or if the two-player version is fun or just possible, or what game you should buy that will be as much fun now as Clue was when you were nine, the Board Game Geeks can tell you. No matter your methodology, you owe it to yourself to play better board games.