Gateway Board Games That Aren't Monopoly
When my husband and I started dating, we were both in college and on tight budgets. Date nights were getting expensive, so while we were on a traditional date one night, we had the bright idea to play a board game for our next date night. The only stipulation was that it wouldn't be Monopoly. I always hated Monopoly. That weekend, I got to John's apartment, raced up 3 floors of stairs, and when I walked inside I saw a brand new never-before-seen-by-me board game set up on the coffee table. All he had to tell me was that it was a game based on disease outbreaks and I was sold--I have strange interests. He explained the rules to me and we started playing. Much to our content we absolutely loved it. I think we played it three times that evening. Since that night, we've expanded our collection to over 50 individual board games. I know not everyone will want to grow a collection of board games, but I think if you tried some of our first games you'd be hooked, too. John and I discuss our "gateway games" quite often. So if you're wanting to try something new, or you feel like starting a new obsession, make note of this post. Full disclosure: you'll see no Monopoly or Life or Clue. One thing you'll notice about all of these games is that they have super unique and fun themes. 
5 Gateway Board Games
Pandemic
The board game I referenced in the intro is called Pandemic. It's a co-op game which means instead of competing against the other players, you're on one another's team! As someone who tends to get super competitive--seriously, just ask my family--this is a godsend because I don't get mad if I lose. If I lose, so does everyone else. Basically, there are diseases popping up all over the world and you and your team are trying to stop outbreaks from occurring while you're looking for cures. You work together with your team to move around the world, eradicate diseases in different regions, and find cures. Once a cure is found, work really hard to get rid of that disease because once you do - it's gone forever! Find cures to all four diseases and you win the game. 
Who Should Play Pandemic?
If you're a science nerd who loves a good theme, you'll totally dig Pandemic. What's more bad-a than curing the world of all its disease? Nothing. If you're super competitive and losing puts you in a bad mood (looking at myself on this one) you'll like this game, too. Because it's co-op everyone loses together or wins together! If team work is your strong suit, or you're looking to improve your teamwork, this is the game for you!
Escape
Escape wasn't one of our first board games, but John and I both see its addictive properties. Escape is a timed, co-op game. If you've ever wanted to be Indiana Jones, here's your chance. You're in a temple that's trying to kill you and all you have to save yourself are 5 little dice and the occasional help of your team mates. One of the reasons I love Escape so much is that it's so quick. Escape is the perfect weeknight game because every single game takes ten minutes or less--always--because it's on a timed soundtrack. The track starts with birds chirping and ominous music, then you hear a creepy voice say "ESCAPE!" and you roll your little heart out. There are two times in the game where you're prompted to head back to the starting tile. You have to make it back before the music stops or you lose a die. Dice are incredibly important to the game and losing just one will decrease your likelihood of getting out of the temple alive... and remember if one of you dies, you all lose! 
The entire game is powered by dice rolls. If you want to move to a new space, you have to roll the symbols that are on that space. You also add tiles to your game board to explore. You have to roll certain symbols to do this. There are various other things you need particular symbols for, too. For instance, there are curses that find you and you can't get rid of them until you've rolled the symbols that are on the curse card. For example, one curse causes you to "lose a hand". You have to roll with one hand only until the curse is lifted by rolling 3 keys. If you never roll 3 keys, the curse sticks. 
From left to right, the symbols are: fire, key, running man, gold god, black god. The gold god exists for the simple reason that you need to roll a gold god to reroll a black god. If you roll a dreaded black god, that dice is stuck until you have a gold to erase it. If you're in the same room with another player, you can use each other's gold gods as if they were you own. One gold god erases two black gods.
Who will love Escape?
If you've always wanted to channel your Indiana Jones and you fancy fun music, you'll love Escape. Escape is also great for players on a time constraint. Sometimes it's hard to commit to an hour long board game, but with Escape you know that every game will take ten minutes or less. I also think adrenaline junkies will love Escape. It's super fast paced!
Ticket to Ride
...or "the train game" as some of our friends have so affectionately nicknamed it. Ticket to Ride is a super simple game that is set in the railroad boom days. Unlike the two games mentioned above, Ticket to Ride is not a co-op game. It's every person for his or her self! You start by drawing cards that give you railroad jobs. These jobs are to build a railway from point A to point B. You get points if you accomplish this, but if you have a card that you don't finish, you lose those points in the end. The game board has dozens of colored sections. To build a railroad on a section, you must play cards that match the color of that section. For instance, if a segment has 4 red rectangles, you must play 4 red cards to place your train cars there. The goal is the make a "train" from point A to point B and then, maybe some other places as well. For the really ambitious players, they may even throw a point C and D into the mix! 
Ticket to Ride seems simple and straight forward, and it is, but don't let that be confused for boring. This board game can get intense. Sometimes, another player takes your path and you have to find an alternate route! Other times, you just can't draw the right colors so you can't move your railway along. Ticket to Ride can also induce "analysis paralysis" where you think-think-think about dozens of moves before you actually make one. ... So, simple? Yes. Boring and easy? No way!
Who needs to hop on the train?
Ticket to Ride is perfect for larger groups! You can play up to five players and the more you add, the more ferocious the competition gets. This board game is also perfect for people who are just wanting to get their toes wet with strategy board games.
Takenoko
Takenoko is just about the most adorable game on the market. Who wouldn't want to play a game about pandas? There are various ways to win Takenoko and each player chooses their own path. Much like Escape, you add tiles to the board as you play which expands the playing area. Depending on how you lay each tile, you can potentially earn points. You use the gardener to grow bamboo, and the pesky panda comes right behind and gobbles it up, sometimes to your benefit. Points are scored by objective cards, and there are 3 different types. You can earn points by collecting certain colors of bamboo, the height of bamboo grown on certain tiles, and/or creating certain patterns in the tiles as you lay them. Each player gets two actions per turn and a bonus dice roll. The extra action comes from the die, and which symbol it lands on: a circle gets you one more action, rain allows you to choose a bamboo shoot to add to your inventory, wind allows you to perform the same action twice, lightening lets you move the panda wherever you wish, and the cloud gives you a tile token. If the die lands on a question mark, you get to choose!
Who should eat the bamboo?
Takenoko is definitely a game for those who have a thing for theme. It's simply a game that plays rather quickly, despite the many pieces involved. There's a bit of mystery involved in Takenoko, too, because each player is working towards a secret individual goal. Takenoko is simple enough for anyone to get involved, so that's why I recommend it for a gateway board game for anyone.
Dominion
Dominion was our second game, and if we're getting technical, it's not a board game. It's a card game. However, it's in the same camp as a board game, so Dominion gets thrown in. Dominion is all about trading cards for victory points that allow you to take over "the dominion". Money and action cards that you collect allow you to purchase other cards. The ultimate goal is to finish with the highest amount of victory card points, but the path that each player takes is completely unique. 
There are many different forms of Dominion and quite a few expansion packs you can add to the main box. The basic Dominion game comes with 25 different action cards (called Kingdom cards), but you only use 10 at a time. It's fun to mix and match the kingdom cards because each game will play differently depending on the cards available. 
The length of Dominion really varies by the game. The game ends when all of the "province" (6 point) victory cards are taken. Winning the game typically comes down to whoever can accrue the most money and province cards the fastest.
Who will rule the kingdom?
People who love variety will adore Dominion. Since there are 25 kingdom cards in the base game, and you're choosing 10 randomly, there are thousands of combinations. Optimal strategy will change with each game which gives Dominion excellent replay-ability!