I've been in a few groups in my history of gaming, and I've liked them all. The last group I played in had very intellectual and cheeky style. Half the players were nice girls, so there wasn't too much trash talking or bad mouthing or sexism. What I most enjoyed about was the vast knowledge of medieval world one of the girls had. I'd call this style "Cheeky Expert".
Right now I'm playing in a group where most of the players are engineers; and devotes ones too! So our game-time is consumed with highly technical details and nothing is skipped as a down-time. If you want to craft an armor, you really have to go through step by step what you do and really use your own knowledge. Not the one that character has. I call this style "Detail-lovers United"
But one of my favourite one was my very first group. Few older guys with little academic background and lots of life-experience. All the "boring details" were skipped and the play was simply concentrated of violence and survival and lots of dark humour with sexism and political incorrectiness. I really loved this style because quite frankly geekiness, non-directness and neurotic "lolcatz"-style "funniness" just pisses me off. Especially in roleplaying. I like that the game is open and direct and there is no competition that who is the cleverest little bastard of the table. Where as engineer-students of "Detail-lovers United" can know a lot about intricities of sword-fighting and historians of "Cheeky Expert" can lecture about the socioeconomic infrastructure of medieval history, it's still nothing compared to a DM that has actually bar-fighted his whole life and can tell us honestly how it feels to have your face smashed in. You can't study that from a book. I call this style "No-holds-barred"-gaming.
And I'm really happy that soon our group will be united again, even though it will be on Skype
So please guys, tell about your groups?