  We provide a census of the apparent stellar angular momentum within 1 Re of a
volume-limited sample of 260 early-type galaxies (ETGs) in the nearby Universe,
using integral-field spectroscopy obtained in the course of the ATLAS3D
project. We exploit the LambdaR parameter to characterise the existence of two
families of ETGs: Slow Rotators which exhibit complex stellar velocity fields
and often include stellar kinematically Distinct Cores (KDCs), and Fast
Rotators which have regular velocity fields. Our complete sample of 260 ETGs
leads to a new criterion to disentangle Fast and Slow Rotators which now
includes a dependency on the apparent ellipticity (Epsilon). It separates the
two classes significantly better than the previous prescription, and than a
criterion based on V/Sigma: Slow Rotators and Fast Rotators have LambdaR lower
and larger than kFSxSQRT(Epsilon), respectively, where kFS=0.31 for
measurements made within 1 Re. We show that the vast majority of early-type
galaxies are Fast Rotators: these have regular stellar rotation, with aligned
photometric and kinematic axes (Paper II, Krajnovic et al. 2011}, include discs
and often bars and represent 86% (224/260) of all early-type galaxies in the
volume-limited ATLAS3D sample. Fast Rotators span the full range of apparent
ellipticities from 0 to 0.85, and we suggest that they cover intrinsic
ellipticities from about 0.35 to 0.85, the most flattened having morphologies
consistent with spiral galaxies. Only a small fraction of ETGs are Slow
Rotators representing 14% (36/260) of the ATLAS3D sample of ETGs. Of all Slow
Rotators, 11% (4/36) exhibit two counter-rotating stellar disc-like components
and are rather low mass objects (Mdyn<10^10.5 M_Sun). All other Slow Rotators
(32/36) appear relatively round on the sky (Epsilon_e<0.4), tend to be massive
(Mdyn>10^10.5 M_Sun), and often (17/32) exhibit KDCs.
