Trends come and go, but no other movement in art has yet proven to have the staying power and influence that the Renaissance lays claim to, namely regarding aesthetic qualities. I think this might be for a reason that, though a bit controversial, seems fairly self-evident. I'm referring to objective beauty; At least to some degre. While there are exceptions to anything, beauty seems to be something that's capable of transcending all culture and all bias. Flowers are beautiful. How many people would argue with me on this (Dick Cheney doesn't count)? Even a big tough biker dude will admit this, depending on who's listening. The point is the Renaissance was focused on this type of beauty to a large extent -- Something that basically all human beings can observe and recognize as beauty. Standards of beauty fluxuate, yes, but only to a certain degree. The real question for art in the 20/21st century seems to be "What is beauty?...Is beauty important?...Should beauty be our aim?" Whether or not beauty is what's important to art critics or trend hoppers, it has always had an audience in the art world. And I believe it always will. The human form, within a certain range of proportions, will always be beautiful. Flowers will always be beautiful..and so will sunsets. It depends on the time period, however, whether a few splotches of black paint on a dead rabbit and some chewing gum is a beautiful image to anyone, let alone a great number of people. I believe this can also be said for much of Picasso and De Kooning's famous works, for example. But is beauty important? How important? Regardless, timeless beauty is important to enough people that there has always had an appeal. Renaissance artists focused heavily on achieving objective beauty (universally appealing) by mastering elements of design and undertanding how to convey beauty in a universal visual language. This is something that will always be recognized and appreciated by a large number of people, I think.
Beyond reaching a universally appealing standard of beauty, the lasting relevance of the Renaissance can be attributed to the particularly relevant theme of Christianity. Although not all Renaissance art was of a Judeo-Christian theme, it seems that as much as half of it (guessing) was, and many of the most famous works from that time are based on familiar bible stories that many modern people still highly regard.
Do I like Renaissance art? Yeah, I can dig it. Where would we be without it?