So there are "board games". Unfortunately, when you say "board games", somehow Scrabble, Monopoly, Settlers, Risk, Bang!, Betrayal, and Catch Phrase all get lumped into this same category. This makes it hard to disambiguate sometimes. I think there should be at least 4 very different categories:
1. Party Games: Catch Phrase, Identity Crisis, Scattergories, and I guess Cranium and Apples to Apples
2. Card Games: Bang, Bohnanza, maybe even Dominion
3. Strategy Games: Settlers, Puerto Rico, Agricola
Now these are on a pretty easy axis: complication (aka nerdiness). Puerto Rico is good to play with your programmer bros, Catch Phrase is good to play with 12 random people at a party and/or your family. And that's the defining characteristic of each category. The card/board distinction seems somewhat coincidental (although maybe not but I'll get into this later).
But the fourth category is word games: Scrabble, Boggle, Bananagrams, Snatch It. The defining characteristic of these games is that they depend on how well you've memorized the English dictionary. And in how many forms you've memorized it: can you come up with an 8-letter word that starts with W? How about a 5 letter word that includes C, A, T, and 2 other letters? (and how quickly?) And because these games are so focused on this one skill, it's hard to place them accurately on the complication axis. Some really nerdy folks don't like them, some totally non-nerdy folks do.
(I like them a lot. They make me feel flowy, and like I'm really honing a skill. If strategy board games are like weightlifting and party games are like running, word games are like pole vaulting. Or learning a language.)
So if the question is "do you like board games?" I think my best answer is "yeah, I'm about a 2.2 on the complication scale, and I love word games." Incidentally, if you ever want to play word games, I'm down.