Watch Wil Wheaton and friends play board games. It's funny, informative and may just inspire you to break out your table top games again.

In 2014
SpearmintFur:

I went to Gencon (big 'ol board gaming/RPG convention) and Wil Wheaton was there. Now me and the people in my gaming group are huge Wil Wheaton fanboys, we will talk in depth about the new episodes and reference jokes from episodes of Tabletop, so I had to contain myself when I saw him at Gencon eating a sandwich. They had some booth where he was playing games, he was setting up to play 7 Wonders. In case you're wondering, he's not a special guest or anything - he goes like an ordinary schmoe, playing board games like anyone else. He won't do photos or autographs, though he was nice to agree to photobomb a photo a fan took that she wanted with him.

If your experience with board games is horrible memories of Monopoly, check out Tabletop. There's a few people online who play board games but Tabletop at least has interesting people do so. Though as a warning, sometimes they screw up big on the rules so if you're using this as a way to learn a game, be forewarned.

Some thoughts on table top / card games:
clu:

Good:
Dead of Winter
Small World
Lords of Waterdeep (with expansion)
Caverna
Five Tribes
Love Letter
Munchkin Adventure Time

Bad:
Settler's of Catan
Really, anything with "Catan" in the title

smith:

I also like Camel Up, Five Tribes and Caverna.

SpearmintFur:

Yesterday I had written up a well thought out comment, but I managed to accidentally close my entire browser window, so I'll try again.

Catan isn't awful, it's a decent game to introduce to people who think board games are just Monopoly, Scrabble, the Game of Life, etc. I personally enjoy playing it with a mini-expansion they came out with, "Frenemies of Catan." It's a little expansion where you earn chits for doing things that don't totally screw other people over (like accepting a trade at a 1 to 1 ratio, placing the robber such that it doesn't affect anyone, etc.) which in turn can be used to get resource cards, development cards, even VP. As there's one lady in my game group who's very cutthroat at Catan, this helps makes the game enjoyable but not too dull. But overtime, you'll realize there are far better games than Catan.

First time I played Lords of Waterdeep, I wasn't too crazy as the mechanics are very generic worker placement with a D&D theme tacked on. However, I played it again and I found it still was entertaining, albeit a bit generic. I would recommend this to introduce people to worker placement games (unless they're super averse to your standard fantasy RPG environment) or to get RPG players into Euro-games.

Love Letter is fun, portable, and easy to learn, though some people are turned off by the theme (sending love letters to a princess). If that's not your bag, there are other versions out/coming out (like a Batman one) but there's also Lost Legacy which has many of the same mechanics (and it's by the same designer) but it's got a sci-fi theme and if you get two of the sets of it, you can play with up to 6 people (as opposed to 4 with Love Letter).

One game I absolutely loathe though is Smash Up - the idea is that you're fighting against various smash ups of various nerd type genre characters (zombies, ninjas, pirates, aliens, etc.) and trying to take over bases. It's similar to Munchkin except at least with Munchkin, there's some element of cooperation and at least you get a chuckle out of cards like the Ether Bunny or the Gentleman's Club. With Smash Up, nothing happens and then it takes 30 minutes to resolve the effects when everyone else plays a bunch of cards all at once to claim a base. Maybe it's because a majority of my gaming group wants to play this each and every time we meet up.

I need to try some of the other games you mentioned. There actually was a Tabletop edition of Dead of Winter released, with Wil Wheaton, Felicia Day, etc. Caverna sounds good as well, I hear it's like Agricola but better (not far off given it's by the same designer).

I'm mostly into heavier Euro-games when I can get them to the table. I'm a big fan of Alien Frontiers - it's a sci-fi worker placement game with dice, but it's nice because you utilize different combinations of dice in different ways and it's not just a matter of rolling high or rolling low like in most games. Also the components are amazing. I also love economic games - I love my 60s version of Acquire and Power Grid is my favorite game. I also like Modern Art - it's an awesome auction game, though it's been out of print for years. Managed to snag a copy off BGG for not too much.