I've been researching connections between anarchism and art for the past few years and the relationship is definitely interesting. What I first needed to realize was that my conception of "art" had to be broadened beyond the "Fine Arts" to get at the most lively aspects of anarchist art (and culture) happening now or in the past. Oddly enough, it didn't dawn on me until half-way through all this searching around that Anarchist Art is a huge phenomenon when it comes to music and the anarcho-punk subculture seems to actually be growing (see www.anarcho-punk.net). Of course, that isn't what most people interested in this question are probably thinking about when they consider the phrase "anarchist art".
Interestingly enough, if you check out theanarchistlibrary.org ...there is a small section on art or aesthetics in relation to anarchism. The theme running through most of the articles I've read on there has either been the sort of Situationist critique of "Art" (wanting to suppress "Art" and realize art as a part of every-day life for everyone); or, some rather unimpressive attempts to conceptualize what an anarchist aesthetic could/would be or has been. Going further, there has always been a lot of poster art (illustration) and zine covers by anarchist artists, there is graffiti, there is puppetry, and there are many other arts and crafts promoted by anarchists for propaganda purposes (note: CrimethINC). But, still this is not exactly what I was really trying to find out about in my research, and probably not what other anarchists who are also "artists" are going to look for in an answer to this question. Though, these anarchist uses of arts/crafts are definitely purposive.
A particularly interesting paper I read (I don't remember where) was focused on the Socialist Realism that emerged out of Russia (and was held up by the Bolsheviks as sort of "the" socialist art) and from there trying to imagine what an anarchist school of art might imply. I believe the conclusion was ultimately that Socialist Realism had some very obvious authoritarian notions behind it, and that an anarchist art would probably have to be too pluralistic stylistically for the way anarchists relate to representation. In other words, anarchists probably won't ever develop some sort of specific "art" (aside from the art of revolution!) in the fine arts sense and that is likely for the best.
The deeper question behind "What is anarchist art (ever)" is a question of Representation and the way anarchists have historically critiqued representation in politics, and the arts. I would assume that because of the violence done to those who are represented in art (workers, oppressed identities, etc.) when they aren't representing themselves... an anarchist approach to art would be similar to an anarchist approach to politics: those who wish to represent themselves ought to represent themselves without the mediation of the (artist/politician). And this is where the question really does come back to the sort of post-Situationist critique of Art, the Museum, etc. as a commodity, as an alienated and alienating practice, and ultimately as the creation of Spectacles to be consumed uncritically by "masses". Along with that, I believe that the response ought to be the suppression and realization of art.
After that it becomes a very heady question and ought not to be summarized so simply. There is always art as self-expression, which I don't see a problem with if it can also be practiced in a way that does not contribute to the capitalist art markets (especially in music), or art as group-practice which is a completely different direction and is somewhat like art-making as cultural ritual (for anarchists), the art-work or work of art itself (the product) having much less value for the community practicing this than the process itself. Perhaps art as therapy could be of beneficial interest to these questions.
So what is anarchist art today?
To make a long story short, the other answer to this question (Greece) is pretty appropriate. Anarchist art today is the practice of anarchist principals and the work of that art is the changes in daily life and in society generally that result. The story about the park in Exarchia that was going to be "re-developed" under the auspices of some capitalist bastards there defiantly being obstructed by anarchists and subverted to serve the purposes of the Exarchia community is likely anarchist art today's finest.