What's the biggest obligate anaerobic organism discovered till now?
There are three worms which have been found in the sediment of the mediterranean seafloor, which not only live without oxygen but also do not tolerate the exposure to oxygen. They belong to the metazoans, for more details see either the report (reference 1) or the original article (reference 2). They reach a size og about 1mm.

References:


Scientists discover first multicellular life that doesn't need
oxygen
The first metazoa living in permanently anoxic conditions