Do I think there is "a" counterculture today? No, ... I think there are MANY countercultures.
[Further, I find it interesting that many people here immediately jumped to the conclusion that the student was referring to the United States! This may not be the case! I'm sure the countercultures in places such as the far East as well as the Middle East (among many others) differ greatly from the countercultures in my own country.]
I consider a counterculture to be a group that does not meld within the established culture of a region. My mind returns to the New York of the turn of the century (1900) where the city itself was full of countercultures, ... neighborhoods and buildings that housed only one nationality each: language, customs, fashion, etc. As the century wore on, many of these countercultures literally melted into what has become the "melting pot" of America.
As mentioned above, the controversial nature of discussing countercultures appears when one enters the realm of religion and race. Are the large Amish communities in both Pennsylvania and Ohio a true counterculture? How about the large pockets of Jewish people living in South Florida? One could argue that at least some Hispanic communities, Middle Eastern communities, and African American communities harbor a counterculture today. Does Harlem in New York City house a counterculture? Does Miami, Florida house a counterculture?
It is fascinating to hear about the thoughts above regarding even things such as sexuality and tattooing as comprising a counterculture. I have even heard that the deaf have their own counterculture, ... so much so that deaf parents are denying their children cochlear implants to keep them immersed in that very culture.
So let me end with this, ... I am glad there are countercultures present in my country! It keeps life interesting and proves quite nicely that even countercultures can exist peacefully in a greater nation.