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[Helmholtz]

My circle of friends and I used to be really into Catan, but I think it's too heavily luck based and don't like it much anymore. It's a great introduction to board games though that should last a while; we played it exclusively for around a year quite frequently. The expansion, Cities and Knights, is better though.
Nowadays I vastly prefer Agricola, and I'd recommend that as long as you don't mind a bit of a steeper learning curve.

 

[echoshifting]

My circle of friends and I used to be really into Catan, but I think it's too heavily luck based and don't like it much anymore. It's a great introduction to board games though that should last a while; we played it exclusively for around a year quite frequently. The expansion, Cities and Knights, is better though.
Nowadays I vastly prefer Agricola, and I'd recommend that as long as you don't mind a bit of a steeper learning curve.

"A bit," he says. ;p

Agricola is great but you need a highly motivated crew of veteran gamers to get into it. I only ever get to play on iPad...I can't even get my wife to go through the app tutorials, and my gamer friends turn their noses up at the theme, the setup time and the dense rules.

 

[emag]

Among lighter games (not much more complex than TtR or Catan), I'd recommend:

Hanabi -- One of the few cooperative games that isn't effectively solitaire; each player (2-5, best with 3) has hidden information and can communicate it only via particular actions
Lords of Waterdeep -- Worker placement game that's good even if you ignore the D&D (Forgotten Realms/Sword Coast/Baldur's Gate) theme
Medici -- Classic auction game for 5-6 players (try the similar Ra if you play with 3-4)
The Resistance -- Social deduction/bluffing game for 5-10 players; similar to Mafia or Werewolf, but much more structured.

If you're looking for something more challenging, Race for the Galaxy is an exceptional card-driven, engine-building, racing (not in the literal car/running sense) game. It's up there with my favorites like Age of Steam, Princes of Florence, and Battlestar Galactica.

 

[Wolfgunblood Garopa]

Terra Mystica
http://boardgamegeek.com/boardgame/120677/terra-mystica

It's awesome. I think it's better than any of the games mentioned here, worth every penny.

 

[Cth]

Forbidden Island. $15. Cooperative game with great components.

Another good one!

If you have an iOS device, a lot of these are also available there.. so you can see if you like it before dropping a lot of cash on the larger versions.

Here's another good resource thread:
http://www.neogaf.com/forum/showthread.php?t=468889

If you're open to card games, I'd second Cards Against Humanity and add Fluxx.

EDIT: (adding more recommendations with iOS ports)
http://boardgamegeek.com/boardgame/3955/bang
Bang! (2002)

http://boardgamegeek.com/boardgame/28396/its-alive
It's Alive

 

[ultron87]

Terra Mystica
http://boardgamegeek.com/boardgame/120677/terra-mystica

It's awesome. I think it's better than any of the games mentioned here, worth every penny.

I definitely need to play that as some point, but that seems like a pretty difficult leap in terms of complexity if you're coming from Ticket to Ride.

 

[t-ramp]

If you want to play a game with some complex interactions but where you aren't directly in conflict with everyone else I'd check out Seven Wonders or Dominion. These involve selecting cards and building up a tableau in front of you that turns into a machine that scores you points.

These are both great games.

 

[The Right Deal]

Seven wonders is a great gateway game, simple, short and fun. A little light on interaction, though.

 

[Experien]

Forbidden Island. $15. Cooperative game with great components.

The same people made a "spiritual successor" called Forbidden Desert. I enjoy it and everyone that I've had play it, they say they like it better. Very similar idea but some substantial differences to make a more fun experience. Also everyone's special abilities are more useful.

 

[Wolfgunblood Garopa]

I definitely need to play that as some point, but that seems like a pretty difficult leap in terms of complexity if you're coming from Ticket to Ride.

For sure. It takes a few games to get a handle on it, but once you grasp the basics there's a ton of depth that you don't feel you necessarily need to know right away. It's not as overwhelming as Agricola is at first.

Another great one is Spartacus: A Game of Blood and Treachery. This game has a lot of player interaction as far as dealing and screwing each other over. Awesome game.
http://boardgamegeek.com/boardgame/128671/spartacus-a-game-of-blood-treachery

 

[Helmholtz]

"A bit," he says. ;p

Agricola is great but you need a highly motivated crew of veteran gamers to get into it. I only ever get to play on iPad...I can't even get my wife to go through the app tutorials, and my gamer friends turn their noses up at the theme, the setup time and the dense rules.

I dunno. I've explained the game to complete newcomers (who only played Catan before), and they understood most of the fundamentals after around 20-30 mins of explaining. It's a game you learn more by playing though I think. There are definitely a lot more rules. To be honest, the game mechanics are fairly simple, it's the card decks that make it more complex. I really like the depth that the game has though. Sadly the rule book is pretty bad.
The main fault I have about Agricola is that it takes many games for people to become good at it. It kind of sucks when I'm playing with a mix of people who have played it a lot and complete newcomers, because the newcomers practically never have a chance at winning. A game like Catan is more luck based, allowing everyone to have a chance of winning.

 

[linsivvi]

This is my personal favorite, Saboteur:

 

[Exile20]

Will buy Smash up and forbidden island or desert.

Also maybe Pandemic on the brink.