No, in today's world art is not for privileged people only. Sure, you can bid at Sotheby's for original Picasso's for thousands or millions of dollars, or you can support today's established and emerging but immensely talented artists who are trying really hard to make a living from their artworks.
For example, at the online art gallery artsrevo.com, there are original paintings for sale, sculptures, handmade prints and photography made by real artists, in prices under $100 for small artworks or $500-$1000 for enormous oversized wall art that you can use as a room centerpiece.
Many regular folks are buying original art at these prices, especially when they are moving into new homes, or as creative gifts for family.
You can also go even cheaper and buy mass-produced reproductions on Ebay by poor artists working in sweatshops from China, but that's not a good investment idea (original art always appreciates in value unlike mass or machine produced paintings or prints), and beware of scams and fake reviews/comments! Similarly, "art" from chain stores like Walmart or Pier 1 will never have any real value, since it is only a duplicate which many people own. And actually for some of the bigger artworks from these chain stores, you can find a cheaper and original artwork of the same size on sites like Artsrevo.