As it was previously stated, there are quite a few out there.
Balder - Silverlight 3D library:
Java and Javascript were not mentioned. @maffel touched on that.
Processing is easy to
get started with. The only problems I see there are the annoyances of Java applets(java runtime ubiquity isn't great, plus you get the annoying 'Trust' dialog as you will be using Sun's JOGL bindings).
You could try WebGL. Dennis Ippel wrote an WebGL exporter for Blender.
The advantage is you will not need any plugins/runtimes, but the disadvantage is
that only a few browsers currently support WebGL as it is experimental. It takes
a bit of setup to get something on screen.
Mr.Doob is working a javascript 3d engine, but currently there isn't
support of importing 3d models.
With Flash, there a lot of options out there. There are examples
out there for what you need using Away3D.
Because Away3D can do what you need, is open source and actively developed I would recommend it.
Other options were already listed(Papervision3D, Alternativa3D).
Yogurt3D is new and seems to handle a larger poly count:
They aim for a syntax similar to OpenGL.
Loading and animating a model seems to be possible using different technologies(Flash,Silverlight,Java,WebGL,etc.), so it depends on the
target you're trying to reach and any other technology/cost constraint
from the stakeholder.
HTH