I have to say that, technically, for something to be a 'Renaissance' it has to be harking back to a previous era of culture (usually classical but I can't see any reason why that should be immutable).
I don't see very much being revived at the moment, in fact I think we live in quite a culturally iconoclastic era- not that there's, necessarily, anything wrong with that. Was 2012 a better year in film than 1962? Probably not especially. Was it a better year in art? Was it a better year in music? Was it a better year in literature? I think it's hard to justify the idea that we're living in a period of particularly outstanding culture. Yes, some of it is very good, but I don't see a radical difference in quality in recent years.
It's also worth noting that Renaissances tend to occur for historical reasons. The Italian Renaissance, which sparked the whole process, came about because of the rise of humanism which allowed classical texts to have doctrinal value. In an age where all literature being produced was ecclesiastical, the introduction of classical influence was a massive change and happened very quickly. If we look at my absolute favourite Renaissance, the English Renaissance of the 16th Century, we see that within 20 years, the politics of England had changed so significantly (from the late medieval period of the Wars of the Roses to the early modern reign of the Tudors) that it was possible to facilitate these advances. What caused it? The protestant reformation and the establishment of the Church of England, which allowed writers like Sir Thomas More (even though he is a Catholic humanist) to write tracts that have profound literary value, and ultimately the period gave rise to authors like Spenser, Marlowe, Donne and, most importantly, Shakespeare.
So, no, I don't think we're currently in a cultural Renaissance and I would doubt whether that term will ever really be appropriate again. But that's not to say that we shouldn't take pride in the 21st century's cultural output.
