That being said, maybe you're fortunate enough to be in a position to teach a game to someone who has never played a hobby boardgame before. Here are some ideas, and my personal choices, for games to try.
The best reason I can give for Tsuro making this list is watching a friend's 6 year old daughter play this game and win. She's not a gamer in any way, but she loved making paths and staying on the map as long as possible. Tsuro isn't deep, but that's why it's a perfect game for non-gamers. There's a lot of luck, but also some strategy. Tsuro also gets major points for being quick. For more info on Tsuro, read my review here.
I like introducing Dominion to card game players, ie Magic, Pokemon, or even traditional card games. The strategy in Dominion can take awhile to see, but it's another quick game most of the time, and the majority of the rules are on the cards so complexity in any given game is minimal. Dominion is a game that draws people in because it isn't overly complicated, but there's a lot of variety.
#5 Zombie Dice
Zombies seem to be a big crazy lately, so why not a Zombie game? Zombie Dice is a quick game where you're trying to eat brains without being shot too many times. Ultimately it's a push your luck game, but it's easy to learn, has those stand-up and cheer or groan die rolls, and that makes it great fun.
#4 Ticket to Ride (US Version)
Ticket to Ride has some strategy, and it may be a little overwhelming for new players, but the theme does a good job of drawing people in. The great thing about TtR is that any given turn isn't that involved. Instead, the game requires an overall strategy, with the ability to adapt to the occasional blockage. For more info on Ticket to Ride, read my review here.
#3 Flash Point
This is the best cooperative game I've played with new people. People seem to have an instinct of what to do to fight a fire, they just need to be told the specific rules of the game. It does help to have someone read the rules and know the game, but Flash Point has a flow that makes logical sense. For more on Flash Point, read my review here.
I like to describe Dixit as Apples to Apples for people who want to be more creative. That being said, you don't have to be immensely creative to enjoy the game. Dixit is all about giving a subtle clue about a piece of artwork in your hand. Then everyone plays a card they think matches the description. Everyone then guesses which card they think is yours. The trick is that you want someone to get it right, but not everyone. Dixit is a great party game, I've had amazing success introducing it to all types of people, and everyone has fun trying to guess, and getting people to not guess their card.
#1 King of Tokyo
This is one of the best dice games I've ever played. The rules are simple, it can be taught in under 3 minutes, and every game feels different enough to keep it interesting. The theme of beating up other monsters and taking over Tokyo is great and enjoyable, the game pace is quick and keeps everyone involved even when it isn't there turn. For more on King of Tokyo, read my review here.