Can today's paintings be as famous as Renaissance paintings?

As other people have said, most of the popular modern art we know is rubbish from dada and pop art onward. 

However, a few years ago I visited the National Portrait Gallery in London. Some of those paintings were exquisite in their detail and skill of execution. I would think some of those will be famous eventually. 

There are some very well done paintings that are done in our time I quite enjoy. If their painting would last 500 years I'm sure they would get recognition for their work. The reason artist from the past get so much recognition is because the paintings have been around for hundreds of years and there are few paintings of the masters and not just anybody can own one, so they are held in high regard and fetch huge sums of money if they are able to be owned by a collector and not already in a museum. Today's artist's painting end up being copied and printed and anyone can own a print for under a hundred dollars even though the original painting can still fetch a good price. Even now though anyone can get a framed print of most famous paintings and their are some artists that can paint a good copy of an old original for a decent price. But I don't believe anything painting in the past couple of centuries will ever have the allure of the old masters. I don't buy art because I do paintings myself that hang on my walls and they make good gifts as well to friends and family. It seems today that everybody paints, not like centuries ago when painters were few.

Today's paintings do not deserve to be as famous as Renaissance paintings. Picasso, Pollock, Kandinsky, Matisse, Warhol, etc. are babies compared to the Renaissance Masters. 

Good question. They will have to invent a longevity pill so we can find out. You'll notice, though, that the best Renaissance painters were famous in their own day and got paid a lot for their work. They have always been regarded as great painters and still are. Very few 20th century painters are like that. Most of the well-known ones have been pretty controversial. 

If they are not burned, stolen, destroyed or neglected. Sure.

Why not? "Renaissance paintings" where once "today's' paintings.

I think you are questioning the art historical 'canon' (making up the stuff that people decided to appreciate and worth saving / study / hang in museums, buy/sell and entitle 'renaissance' or denoting it as prototypical whatever'ism) You should question that! And than tell me the answer ;-)

Today's paintings are junk compared to those of the Renaissance and Baroque period. In the future, people will laugh at Picasso's, Pollock's, Kandinsky's, Van Gogh's etc. crude smearings that are only loved by utter fools. PickAssHole admitted that he was a scammer selling junk to fools. 

It's possible but it would take time for that level of recognition.

Can today's paintings be as famous as Renaissance paintings?

I don't think so. The graffiti is an example. (Drive to be famous is strong. So strong that it is absurd.) The second example is the galleries. (There is so many galleries as is the artists.)

only if they are nekked children