I try to refrain from claiming to support a format, since support entails a strict parsing model that's unsuitable for an end-user product. "Understand" may be a better word; many feeds use broken language, but R3R can still understand them (or parts thereof).
See also the Guidelines and Choosing a Feed Format for authoring advice.
R3R only supports XML attributes when necessary for feature parity with non-XML feeds.
As far as I know, R3R fully understands RSS 3.0.
R3R also fully supports ESF, the easiest feed format that I know of.
RSS 1.0 superseded 0.9, so that version won't be discussed. R3R currently ignores textinput (and sub-elements thereof), though it may be added to future versions. The rest is understood (with the exceptions of the attributes listed above).
RSS 2.0 replaces 0.91–0.94 as the recommended XML-based version. R3R doesn't support many of its elements.
* = being considered for future versions
This is the support status for Atom. Note that R3R does not support the Atom API.
* = being considered for future versions