Greek life is big, but not too big. It provides most of the social life and parties on campus, although off-campus activities can be found downtown, and in other areas, that are unrelated to greek life. I'm in a sorority, which I joined the second semester of my freshman year. It made a HUGE difference on my social life, I went from being rather unhappy at WashU to being very happy with so many new friends and social activities. Now, all my best friends are in my sorority. However, I still have girlfriends that are in other sororities, or aren't in greek life at all. Most of my guy friends, similarly, are in fraternities. Greek life at WashU is far different from what I hear about at state schools. It isn't very time consuming for girls, but is very time consuming for boys. There is no hazing for sororities, but I think there is some hazing for boys (as I think there are at all colleges, unfortunately). WashU tries very hard to eliminate hazing, but actually tries a lot harder for the girls. Sororities are kind of a side activity, but you can be as involved or as uninvolved as you want, which I love. It's a very easy way to get involved on campus!
Two of my best friends aren't in Greek life, and belong to another extracurricular called EST, which is a completely student run emergency service that's on duty 24/7 on campus. That too, is a great organization, which I really recommend if you're interested in anything medical related.
Students live in dorms until their second year (usually) on an area called the South 40, until their junior year when they typically move across campus to "the Village" to live in on-campus apartments. I lived in two very nice, new dorms my freshman and sophomore year, and lived in a less-nice on campus apartment my junior year. Housing at WashU is difficult, although I've personally had a very positive experience with them. I've gotten my first choice for housing all three years, which is extremely lucky, because most of my friends often get their second or third choice. Housing is rather unaccommodating if students don't get their first pick, which as a huge complaint among the student body.
Some traditions that happen on campus include WILD, a biannual concert, which is so much fun. WILD, or walk in lay down, is a concert, that happens all day. It's the one day when WashU parties like a state school, which is about all we can handle. Past performers have included Shwayze, The Cold War Kids, Passion Pit, Method Man and Red Man, and even the Black Eyed Peas way back when. It's a lot of fun.
Guest speakers are big at WashU. We held the last VP debate in 2008, which I really wish I had seen! A big comedian comes once a semester, including Seth Meyers, and Donald Glover. Shows are free...but have INCREDIBLY long lines, so come early and be prepared to wait! It's really cool having famous people perform for free at our school (for students, at least), and I really recommend going to some of the shows. It's a big drawing factor, since WashU is highly respected among many people. Next semester, Sofia Vergara from Modern Family is coming. Unfortunately, I'll be abroad, so I won't be able to see her!
There are also many clubs and other activities, as well as volunteering opportunities and political activism opportunities, that are presented in a fair in the beginning of the Fall semester. I recommend attending the fair if you're interested in becoming more involved, which I also really recommend!