I don't know what the most popular clubs are, but Greek Life is pretty big here - about 25{4a082faed443b016e84c6ea63012b481c58f64867aa2dc62fff66e22ad7dff6c} of the campus is Greek. If you're looking at the people who actually go out and have a social life, the percentage is probably larger.
I am in a sorority (Chi Omega) and it has really helped me expand my social circle and world here at Penn. I've met people that I never would have otherwise and I love all the events we have with frats, the downtown parties we throw, and the bonding I get to do with my sisters.
I'd say the majority of freshmen leave their doors open - I know we did. And even after that, when I lived in an on-campus apartment sophomore year, our door was always open.
Athletic events are marginally popular - "big" games (such as Princeton, the Big 5, etc) are always packed, but only football and basketball actually draw fans. The people who go get really into it, though. Penn usually gets some great guest speakers, so those almost always sell out. We've had Bill and Chelsea Clinton, Whoopi Goldberh, Peyton Manning, etc.
The dating scene at Penn is so bipolar. Either you're casually hooking up with someone (or lots of someones) or you're in a serious relationship - there's no middle ground. This annoys me because I'm not looking for anything super serious but guys won't do the "dating" thing.
I met my closest friends on my hall freshman year, which I think is pretty standard. I've met more through my sorority though, and added people through those people.
On a Tuesday at 2 am, I'm definitely at Blarney (one of our campus bars) playing Quizzo (a bar game that goes on every Tuesday). The game would just be ending and people would be starting to head home. The bar always gets packed and it's so much fun -if you win, you get a $75 bar tab!
Spring FLing is the biggest event of the year - basically a weeklong drunk fest. THe school puts on a carnival in the Quad (a freshman dorm area) with moonbounces, dunk tanks, etc and everyone just drinks themselves silly for a week. There's also a concert - my freshman year was O.A.R. and last year was Ben Folds and Third Eye Blind. Other traditions are Hey Day (where juniors march through campus and seniors throw stuff at them to "initiate" them into senior year - this happens on the last day of classes) and Senior Week (the week in between when finals end and graduation where each day seniors have a differnt event to do).
I would say people party a lot. There tends to be something going on almost every night of the week. Tuesday is Quizzo at Blarney, Wednesday is Sink or Swim at Smokes, Thursday is either Smokes/Blarney or a downtown club event, Friday is more chill just hanging out at a frat or with your friends, and Saturday is big frat party night.
Greek Life is important for those who are in it, but it's not the end of your social life if you're not. I'd say it's more important for a guy to be in a frat than for a girl to be in a sorority.
Last weekend I went downtown for a date party my sorority had, and again the next night for a party thrown by a frat on campus; I also hosted a Beer Olympics at my house.
On a Saturday night you can go see a movie, hang out with friends, go out to dinner at the amazing restaurants in Philly...