As I have just finished 1st year at LSE I think there are several clear traditions I have seen emerge:
Yes, slagging off Gimperial, Strand Poly and Euston Met is a real tradition (as observed in the Beaver newspaper every thursday), claiming to be as good as Oxbridge (I won't enter that mindfield on whether it is true or not), friday night Crush is a must, Wednesday night Walkabout in Shaftesbury Avenue.
I totally agree with other posters who mention Danny Quah, even though he's not in my department all the other students who attend his lectures love his comments despite claiming "he's far to advanced to teach first years", he seems a bit of a legend.
One other tradition I must, must highlight is an unfortunately one, The Socialist Workers Party, (althought you may like to change the "or" in worker for an "an" to reflect their status as I do!). Basically they are a load of whinging old lefties who are annoyed that many left-leaning LSE students still end up in internships for global banks and right wing governments, they stand most days outside the East Building with their "one stockbroker is one too many" banner to illustrate their jealousy that they dont have the skills or ability to be a stockbroker. Definitely a group to avoid during freshers week!