movements i think really need to change the art world, too, in order to be significant. impressionism was not accepted by the broader groups during its time, so they created their own group within modernist criticism, a group which is now accepted into the artistic canon. Likewise, every other significant movement has been at odds with what was prevalent at the time, first priding themselves on being a counter-culture (often flaunting the criticisms of the establishment, as was very much the case with impressionists and fauvists and the like), and then later on becoming a dominant force due to the human desire to establish a legacy and to give something to the world. This of course is a rule with many exceptions, but it holds true in most examples.
What's difficult now is that it is diffcult to determine what is the culture and what is the counter-culture, and as both are ever-chaning it is hard to pull out "significant" movements.
Low art is infinitely more prolific than high art, as it always has been, and is appraised largely on the grounds of aestheticism and psychoanalytical criticism as it pertains to marketing, so one could generalize and say that the establishment is dicated by early-nineteenth century thought processes while the counter-culture consists of all that is neither: "ugly" art etc.
High art is characterized now by a rejection for (and therefor acceptance of) everything under the sun. This unfortunately makes for a rather confused art world that feels stagnant and confused. Even people who are considered "cutting edge" are going back to old ideas while adding little. Matthew Barney has demonstrated that if you eat a high-school level essay on Freudian psychology, shit it out, and put boring music behind it, you will be recognized, despite the fact that freud, shit, and boring music have all existed for generations. He is successful because he capitalizes on the widespread idea among postmodern critics that anything repulsive to the majority of people must be revolutionary (despite the century-old foundations for everytihng he does) and if something is revolutionary then it must be good and if you can't appreciate it then it's your own failing.
I personally believe in a form of collective modernism based largely on my spiritual views. Everyone contributes to a vast pool of human experience, with each stimulus (work of art in this case) yielding an unending number of equally valid interpretations of meaning or lack thereof (as opposed to the idea that a single interpretation - that of the artist - is the only correct interpreation). People who contribute empty, pretentious, even "false" art do so to drive others into a fury in which they produce "real" art in the same way that terrible things happent to people so that they might better appreciate the good things. Without bad art, how could we find anything we think is good? The world as it exists now, with everything uimagineable being both blasted and praised, is an environment which cannot help but yield the best and the worst that the world has seen thusfar, and these will only become more polarized as exposure to culture becomes more and more easy and extensive.