Some of the most popular organizations are publication organization such as with the school's 2 "competing" newspapers the Daily Gazette or the Phoenix, and our mens' soccer team probably has the most successful record.
I have been really involved with Swarthmore Asian Organization (SAO) for the past 2.5 years, which is a group for Asian and Asian American students on campus that focuses on trying to promote social, educational, and political education as well as participation about issues within the Asian American community as well as for all people of color. There are weekly meetings as well as multiple events throughout the year that focus on different aspects of identity politics, group discussions, educational workshops, and social events. One of the major undertakings for SAO is Asian Pacific Islander American (APIA) Heritage month during each spring semester. It is a whole month of events revolving around Asian American issues, where speakers, performers, and student led events and activities go on around campus.
Students in dorms definitely leave their doors open most of the time unless they have a test to study for or are sleeping or really need to study. Athletic events are not that popular amongst non-athletes. There are constantly guest speakers and lectures going on in different departments. The student theater scene is pretty active, and we definitely have a good number of quality productions each year. The dating scene is a little difficult in some ways because of the small size of the school. People do date, but sometimes it is very extreme for example, a couple may constantly spend time together to the exclusion of all other friends, or they may be too busy to ever spend time together.
I met some of my closest friends through the Tri-College Diversity pre-orientation workshop as well as through my classes. I would probably be doing a problem set at 2 AM on a Tuesday.
There are a good number of traditions/events such as Screw Your Room Mate, the Primal Scream (and the newly implemented breakfast at midnight), the Pterodactyl Hunt, First Collection for Freshmen, Sager, many more...
Depending on your course load and weekend, you might party every weekend or only a few times a month. Fraternities/sororities exist but do not dominate the social scene.
I am abroad so I can't really answer the last weekend question...
A non-drinking Saturday night out might consist of going to watch a free film screening, cooking with your friends, going to a free performance, catching the train or taking the shuttle to Philadelphia to go to dinner or watch a movie or a concert.
Off campus I am usually either volunteering in Chester nearby, or going to Philly for a fun outing or to buy things that I cannot get in the Ville.