Paul Butzi has a couple of good posts on the myth of talent over at his blog, Musings on Photography: the first is here with follow-ups here and here. I've commented on the first of those on his blog. His thesis is essentially that innate talent is an overrated notion. There is no way of gauging a person's early talent that will predict whether he will end up successful as an artist. It is only in hindsight that you can recognize talent. Furthermore, this mysterious thing called talent is no substitute for hard work. Given enough determination and practice, even someone who did not think she was talented can develop the skill to make good art. Deciding after a couple of false starts that you have no talent and just giving up on art would be a tragedy, whether you're destined to become another Rembrandt or not. Here's my friend Jayne's great story of how she never thought she'd become a good knitter but then persistence paid off. Her present passion for knitting (addiction, one might call it) means she gets tons of practice and gets better and better. You should see some of the amazing stuff she does (all photographed and shown off on her blog, See Jayne Knit).
Of course as a Christian I believe that there are gifts bestowed by God, including artistic gifts. Some people have them and others don't, or rather some people have certain gifts and other people have other gifts. But I agree with Paul's observations that thinking one has no artistic gifting (or "talent") is no excuse for not working hard to develop it (and even, I might add, to discover it in the first place). Even the most gifted artists have to work at their art. A lot of times an artistic talent can be buried by hurtful (and untrue) comments made to one during childhood by insensitive adults. While it is not always the case, usually you will find in the background of great artists a supportive parent or patron. Mozart, for example, doubtless had a larger measure of gifting/potential in the area of music than most of us do, but he was also fortunate enough to have had a supportive father who took him all over the place to play for and get training from famous musicians. Some artists who have suffered early discouraging remarks have been able to break through that later in life and rediscover and develop their creative gifts. The Artist's Way: A Spiritual Path to Higher Creativity by Julia Cameron helps people do that.