The goal here is to give you some ideas for games that give you different play experiences, work for a good player range, and don't cost all that much money. Consider this the starter set of games. It can be expanded, games can be interchanged, but these are good ones to start with, and games that will give you a good collection.
Now, not every category is relevant to every person, nor is this list comprehensive, but I feel it's a good place to start.
The Short Family Friendly Game
We need a game or two that is short enough to play while dinner is close to ready, or a game before bed on a weekday. Some good suggestions: Incan Gold, Can't Stop, No Thanks!, High Society.
For this, I recommend Tiki Topple. The production quality here is excellent, and the game plays in under 30 minutes, typically closer to 20 minutes, but can be made shorter or longer by changing the point total to win. For more on Tiki Topple read my spiel on it in the Top 42 list.
Every gamer needs a good game they can pull out with a large group of people and have a good time playing. It shouldn't be too long, and certainly not complex, but it should be something to get people talking.
Here, I offer a few suggestions. Apples to Apples is a good one to get people talking. Werewolf or Mafia is great with a group of people who know each other, also great for a large group. Tumblin' Dice is a lot of fun, but it's rather expensive, so it loses out on the Bang-for-your-buck aspect. Wits and Wagers works well for a more intellectual gathering. All of that being said, if you have to own just one party game, Say Anything gives you the best bang for your buck. It's ~$20, you can find it in most Targets and Toys 'R Us, as well as various online stores, and it was designed to get people talking about the questions. It's a great way to get to know other people in a fun and creative way.
I think that a lot of people view boardgames as only competitive endeavors, but there are dozens of games where players are required to work as a team in order to achieve victory. I own several of these games, and I enjoy the ones I have for the most part, but the best one in terms of Bang-for-your-buck is Forbidden Island. It's the cheapest co-op game I own, but it's also on the same level of fun as the rest.
Some other co-op games that would be good for a collection, Pandemic, Space Hulk:Death Angel the card game, Defenders of the Realm.
Team game/co-op with a Traitor
Sometimes you don't just want to work together as a team, winning and losing together, so here's a category for you. For me, three games really stand out for this category: Shadows Over Camelot, Battlestar Galactica, and The Resistance. This category boils down to what you want out of the traitor mechanic. The Resistance is the shortest game, and you're trying to figure out who's against you, so they can't hurt your ability to win. I don't own the Resistance, but it seems like a good time. Shadows Over Camelot is a great theme implementation. The game boils down to finding the one traitor, if there even is one, and deciding when to win certain quests, and what can be lost. Battlestar is pure theme, with some decent mechanics. It's probably the most balanced of the games with traitors, but there's still a lot of luck. My advice would be to get The Resistance. It has a good player range, and it's the cheapest game of the three here.
Here's a category where even the best strategy can be mitigated by how well you can do some physical task. The best known game in this genre is either Crokinole or Pitch Car, but both of these get fairly expensive. So let's take a look at some less expensive dexterity games. Catacombs blends flicking with strategy, but even then it's a bit expensive. Pitch Car Mini is another good option, still pricy, but feasible. Ultimately this category comes down to 2 games for me - Bisikle/Roadsters and Sorry Sliders/Sorry Sliders 2. Roadsters has the better quality components, but Sorry Sliders 2 just seems more fun. There's a lot more you can do in terms of hazards and track arrangement with what comes in the box.
Therefore, the pick for dexterity game is Sorry Sliders 1 or 2.
Random Skills Game
This is for those games that involve some kind of skill that isn't normally seen in games, but that people use in life sometimes. These typically aren't high strategy games, but they have their place on our gaming shelves. Two games come to mind for me: Dixit and Aargh!Tect. Dixit is a game about telling a concise story as a clue so that at least one, but not all, players can figure out which card is yours. You also have to figure out other players' clues when you aren't giving them. This isn't all that abnormal, but the story-telling aspect isn't seen often. Aargh!Tect is unlike any other game I've ever seen. There are two teams competing to arrange pieces to form the building that the manager has. The manager has to give directions to the builders, but the manager has an inflatable club, and can only use caveman language and certain motions. When players get it right they get 1 tap from the club, but when they get it wrong, it's 2 taps.
If cost wasn't an issue, Aargh!Tect would be my choice based on the experience alone. You grow to fear the club coming down on you, but it's all in good fun. Dixit is the cheaper option, and probably better for some groups, so it's really up to you.
2 Player Only Game
There are a lot of 2 player games on the market, and many of them are good games. These aren't my forte since I rarely play only 2 player games, but I have a few I like, and some others I know enough about to recommend. I have four 2-player games that I play every so often: Memoir '44, Mr. Jack, 1960:The Making of the President, and Twilight Struggle. All three games have good parts and drawbacks for me. If you like political games, either 1960 or Twilight Struggle is a good call depending on if you want to focus on US Politics or Global Events of the Cold War. Mr. Jack is good if you're looking for a deduction game, but it lacks great replayability in my mind. Memoir '44 is a good WWII game with pretty good mechanics, and a ton of expansions. From what I've heard, Lost Cities the card game is a great two-player game. It's been described as a great couples game. So even though I haven't played Lost Cities, I'm going to recommend it as the 2 player game to own.
There are three big games when it comes to intro style games, and I don't think you can go wrong with any of the three. Those three are of course Carcassonne, Settlers of Catan and Ticket to Ride. They're all good games, but if I had to pick one that works to teach people about hobby boardgames, I'd have to choose Ticket to Ride. Your mileage may vary of course, but the variety of Ticket maps gives players more options.
Advanced - non brain-burning Game
I suppose we can call this category the next step games. There's a lot of games that could fit in here, but I'll give you a few of my favorites. Small World and 7 Wonders both fit here. Yes, I know a lot of people say 7 Wonders could be an intro game, but I really think it's a next level game. Kingsburg would also be a good fit, though it has a fair amount of dice, it also has strategy. Any of these games would work well depending on your predilections, but my choice here is Cosmic Encounter.
Brain Drain Game
Here's a category for those times when you want to sit down and play a game for 2+ hours and really get into it. I know these kind of games aren't for everyone, but sometimes it's nice to have a complicated game to play. I've personally only played one of these, Agricola, and I enjoyed it. So Agricola is my recommendation. Personally, I'd rather play a variety of games than one brain-burner, but Agricola is still a good one to have around. Some other games that fit the category here: Puerto Rico, Brass, Le Havre, Caylus, Twilight Imperium III. None of these games are cheap, but Agricola is reasonably priced and has a lot of replayability in the box.
This isn't for your traditional deck of cards game, but rather for a game that is all, or essentially all cards. This includes the better CCGs, like Magic and Pokemon, Living Card Games such as Call of Cthulhu, Game of Thrones and Lord of the Rings, as well as deck-building games like Ascension, A Few Acres of Snow, Thunderstone, and my personal pick Dominion. The base game is very reasonably priced, and has 3,268,760 differ possible card sets. I'd say that's good variety.
The last thing that every collection needs is a dice game. There are many games that use dice, but this is for a game that makes dice the main or only portion of the game. There are a lot of good games that are basically just dice, LCR and Liar's Dice come to mind; but the best dice game I've played is Roll Through the Ages. It's fairly inexpensive and has a lot of variety and strategies to it.
Here's the list of my recommendations
- Tiki Topple
- Say Anything
- Forbidden Island
- The Resistance: Avalon
- Sorry Sliders 1 or 2
- Lost Cities
- Ticket to Ride
- Cosmic Encounter
- Roll Through the Ages
If you wanted to start a game collection, or boil a collection down to 12 games, I think this list would give you a good variety of themes, styles, and player range (2-10).
Is this comprehensive? By no means. I don't even own 3 of the games, though I've played 2 of them.
I suppose my main point here is, when you're looking for new games, variety is key. Expansions to what you own are great, and take up less shelf space, so that gives you more of the same type of play experience.
Sorry for the short novel on building a collection, but I feel it's a necessary thing to have.