Harvard and Princeton still have a student deliver speech in Latin in commencement. Anecdotally, since most graduates have no clue what they are saying, someone would hold a sign telling them when to laugh and when to applaud.
I don't know of any others that are quite that bad, but most are pretty flowery. I'm still waiting to get the "rights and privileges" my university promised come with the degree.
Benefits based on having the degree in immigration point systems is a nice example of such a privilege. So is having that university's name on your resume, in cases like Brown where it's a famous name.