Renaissance art will always stand alone in function and purpose. Of course it was a catalyst for artistic method and style. It was a period that provided the advancement that the art world had long needed. Paintings gained depth from the discovery of linear perspective and other visual cue techniques. Sculptures returned to a Roman naturalistic style, bringing more life to all the figures. And architecture moved from Gothic styles back to Romanesque, with rounded arcades and a more horizontal orientational. Overall, architecture was more simplified and restrained.
As for the role of Renaissance art, there are several. First and foremost, the architecture seemed more practical. It served a more general purpose. Paintings were more for a specific population, that is, usually a work commissioned by a family for their home or church. Artists did not paint just to sell or hang their works in a museum. Sculptures, however, were both for the populous and for specific persons/families. Statues were erected in public forums, like those in ancient Rome. But statues and other sculptures were also made for specific churches or households.
As for art in today's society, architecture is still very practical and mostly simplified. Architecture is hard to compare because we do not view it the same as art it was in the Renaissance. Our architecture is meant mostly to serve a purpose or function, not necessarily to decorate an area. However, in recent years there has been a resurgence in designing extravagant buildings, but mostly in cities like Hong Kong, Dubai, and Abu Dhabi. So the practice is not dead entirely, and perhaps its being revived.
Modern attitude towards paintings is mostly for artists to create works for others to buy. Not often are artists commissioned to do work. It's mostly a freelance trade, and each artists is hoping to be recognized for his/her talents by hanging their works in galleries. Most of the art that we use for personal collections, however, are art replicas, or prints of famous paintings. There is also a desire for what I like to call "feel good" art, which are replica paintings of artists like Thomas Kinkade. Much like van Meegeren's forgeries, there is aesthetic value(1), but the art is not worth anything. This is vastly different from the Renaissance art, which was original, and not only had aesthetic value but also value because of the artistic merit.
Sculptures are still used in similar ways, and viewed similarly as well. It's not uncommon for a city to commission a sculpture to honor a former president, other political figure, war heroes, or even local heroes. Public statues in modern era and the Renaissance served a very similar purpose. Abstract art, however, has emerged to be a another means of public art. The use of abstract art to decorate empty space in a forum was unheard of in the Renaissance, mostly because the technique wasn't around. But today we often find abstract art to be pleasing and appropriate to fill empty space. It accents our environment and serves similar purpose as the statues the modern and Renaissance era.
One major difference in art today from the Renaissance is the use of public art in general. It may not be completely recognizable to those who do not have the proper sensitivities to art, but public art is a major part the current art culture. Artists like Banksy use public art as a way to speak out against propaganda. Other artists like Maya Lin use it as a way to make a name, and like the use of statues, use it to honor war heroes . And then artists like Richard Sierra, who are world renowned, are commissioned to create public works because of their name.
Art still serves similar roles today, and it forever will as long as it is meant to be enjoyed and viewed by mass amounts of people. Artists do not want their works kept quiet. They are mostly proud of their abilities and recognition if the best thing for their careers. They want to create works that will garner income for them, after all, hasn't that always been the goal of artists. It may be something one loves to do, but anyone who has no career besides art needs it to be a source of income. Renaissance art stands alone in its purpose because of the change it brought to the art world. But as long as the public finds value in artistic ability, arts most fundamental purpose will always remain the same.
(1) I am not comparing Kinkade's artistic ability to Vermeer's, just the similarity that to some extent Kinkade has aesthetic value.