We present new results from the PHOBOS experiment at RHIC on event-by-event fluctuations of particle multiplicities and angular distributions in nucleus-nucleus collisions at RHIC. Our data for Au+Au collisions at s NN=200GeV show that at a level of 10-4 or less, no rare, large-amplitude fluctuations in the total multiplicity distributions or the shape of the pseudorapidity distributions are observed. We however find significant short-range multiplicity correlations in these data, that can be described as particle production in clusters. In Cu+Cu collisions, we observe large final-state azimuthal anisotropies ν2. A common scaling behavior for Cu+Cu and Au+Au for these anisotropies emerges when fluctuations in the initial state geometry are taken into account.