Well, let's analyze this in sections, shall we? Also, remember, it's my opinion.
Literature
Mostly, I dislike being unable to relate to a character when a book is sort of outdated. For example, when a book is purposefully set in an era the reader is supposed to recogonize as outdated, it's okay (and sometimes quite nice actually) but I do not stand reading books that are old yet are supposed to apeal to modern audiences (or what was modern back then).
TV
The most modern possible in heartbeat. I want to puke in a bag whenever I have to see anything from before the 95's, and even in that situation there are very few good 95's shows (other than Friends, which is awesome). I personally think crap like Rugrats is garbage, but cartoons from this year aren't exactly amazing either (but at least it's an improvement).
Music
Some music influenced by 20th century music is okay, but other than that nothing specifically from that century is good. I like classical music though. (Of course, today's music isn't exactly perfect either. I am going to strangle Rebbeca Black if I ever meet her. But if you search, there are a few gems.)
Films
Like TV, watching anything old is the ultimate form of torture.