I think the artistic methods developed during the Renaissance are what accounts for it's ongoing status. Two methods I think are especially important are methods of perspective and methods of drawing lifelike people.
Perspective effects all artists. Even if you are not using rules of perspective, you may be breaking them. Renaissance artists had to take risks to get it right.
Humanism in the Renaissance greatly effected the human expressions in art. I doubt that humanism wouldn't have happened at all had it not happened in the Renaissance, but it's great that it did. It's fun to think about what art would look like if people still could not get these expressions and realism down on paper.
Who doesn't like Renaissance art? So far, one of my favorite artists is the Roman sculptor Bernini. His amazing sculptures are incredibly lifelike and expressionistic. His "Apollo and Daphne" is very stirring. There is much movement and story in the piece, and you feel like you are in the presence of the doomed-to-treeness goddess herself.
Michelangelo's Sistine Chapel is another classic. Where would we be without that? While the realistic answer to that question is "Rafael's Sistine Chapel", art would not be the same without the masterpiece.