Have you ever had a miscommunication in email? Email is great, but because we are not dealing face to face, we have none of the subtleties of communication to observe when words alone are insufficient. Just as there is no experience like chatting face to face, there is no experience like seeing a work of art in person. Art is a visceral experience.
On the other hand, viewing art online offers convenience & accessibility. You can look at your computer monitor after dinner in your jammies  (something you really can't do in most of the galleries I've visited!) And probably one of the biggest advantages is that you can search through a massive array of styles, subject matter and price ranges all with a few keystrokes. Of course, the down side is that you can also search through a huge range in quality as well, so you kind of have to love a good scavenger hunt!
But the online experience can provide a certain intimacy as well. One can become intimately involved in a work of art through various aspects of the online experience. This includes artist's blogs, information on the website, demonstrations, videos and more. By intimacy I don't really mean people knowing each other's personal life; just intimacy with the artwork and the artistic experience through stories, connections, information about the art, etc. Many online collectors have the advantage of knowing a little something extra about the artwork or the artist. And often unlike some gallery experiences, one can even dialogue more readily with the artist as well.
I show my work both online and in the "real world". They both offer certain benefits to me as an artist, and I think each venue complements the other very well. I also shop both online and in the real world, (yes, for art! and other things too) but more and more I am becoming quite comfortable with shopping online. Of course I want to know that my purchase is guaranteed with a sound return policy and that there are testimonials that speak to quality and the buying experience, so those are things I would look for. But the world is changing and I think soon buying art online will come into its own.