My first experiences with modern boardgames came, as with many of us I guess, with Settlers. We were all very much into video games and a local store (back when you had to walk to a store to actually get a physical copy of a game) carried some board games and RPG's too.
I believe we actually tried the Shadowrun RPG before we got into board games, because we knew the franchise from video games. It did not turn out well. In the first five minutes of the first game, one of the players threw a grenade in a small room, we rolled some dice, we all died, and we put the game back on the shelf for good.
But then they got Settlers. And we played it to death. Today, I can't stand it. I practically loathe the game. But I spent many a night playing nothing but Settlers and back in the day, I enjoyed it a great deal. After Settlers started to wain on us, another friend bought Tigris & Eufrates, and after that El Grande (which remains a favorite of mine). I lost contact with them, but the longing for board games remained. That's when I sought out what information I could find and discovered BGG. It didn't take long to track down and place my first order: Samurai. It looked gorgeous and it did away with the luck of the roll of Settlers. I was loving it.
From there on, my collection's grown a great deal, and so have my tastes. I came from mainly enjoying abstract euros to appreciating some ameritrash games, party games, just about anything goes nowadays.
My favorite games shift a lot. I have a bit of an itch for discovering things, so I don't repeatedly play the same game over and over, but rather taste a little of different pies.