William Kentridge is the first artist animator that I know of whose work was taken seriously by art curators. The first time I saw a Kentridge animation in a museum setting was at the Musée d'Art Contemporain in Montreal. The following year I spotted one at the National Gallery in Ottawa.
Now I'm reading about entire exhibitions (three that I know of to date) dedicated to animation as an art form.
When we change the venue of the delivery, we change the way we interact with the form.
Most animated films are meant to be watched in a theatre, where the audience is captive in their seats and the film runs through from beginning to end. In a museum setting the audience stands in front of the work, free to move on the minute they lose interest. On the other hand, they're also free to stay and watch the film several times over if it really interests them (imagine calling for an encore in a theatre.)
William Kentridge's animations feel like they've been designed to be seen in a gallery setting. They have that particular focus on the texture and gesture of the mark rather than the line playing a supporting role as defining the edges of a shape. It takes time to read these images because they're complex and working on many levels. Perhaps this is why we rarely see his work at animation festivals, or as part of compilation DVDs dedicated to animation. One wants time to watch them, to become immersed in the network of marks that make up the imagery (in addition to following the story.)
This past summer Sarah Lewis and Daniel Belasco curated an exhibition that was presented as a major paradigm shift in contemporary art. Titled The Dissolve, the venue was the prestigious SITE Santa Fe Eighth International Biennial Exhibition 2010.
"The curators will present a new sensibility in the art of our time, a mingling of up-to-the-minute technology and traditional visual arts (painting, drawing, and sculpture) with dance, music, and film. The fundamental form of this new work is animation, uniting the technological (the camera) with the hand-made (drawing)." http://www.thedissolve.net 
The show was at once an overview of animation history going back as far as Edison and the Fleischer Studios, a collection of art animation masterworks including films by William Kentridge and Maria Lessnig, and an introduction to experimental animation by current new voices.
The Drawing Center in Manhatten ran a show of animated short films in 2006 called Analog Animation. This year they are presenting Framed: Drawings In Motion which opens in mid-November and runs until December 2010. This is a collaborative show with Smart Spaces, the not-for-profit art space that uses vacant store fronts as their roaming venue.
More about this show in an upcoming piece.
In the meantime, if you want to pursue animation in gallery and museum settings, arm yourself with a recent dictionary because you may need some fluency with postmodernist terminology.