  [Abridged] We present the apparent stellar angular momentum of 300 galaxies
across the Hubble sequence, using integral-field spectroscopic data from the
CALIFA survey. Adopting the same $\lambda_\mathrm{R}$ parameter previously used
to distinguish between slow and fast rotating early-type (elliptical and
lenticular) galaxies, we show that spiral galaxies as expected are almost all
fast rotators. Given the extent of our data, we provide relations for
$\lambda_\mathrm{R}$ measured in different apertures, including conversions to
long-slit 1D apertures. Our sample displays a wide range of
$\lambda_\mathrm{Re}$ values, consistent with previous IFS studies. The fastest
rotators are dominated by relatively massive and highly star-forming Sb
galaxies, which preferentially reside in the main star-forming sequence. These
galaxies reach $\lambda_\mathrm{Re}$ values of $\sim$0.85, are the largest
galaxies at a given mass, and display some of the strongest stellar population
gradients. Compared to the population of S0 galaxies, our findings suggest that
fading may not be the dominant mechanism transforming spirals into lenticulars.
Interestingly, we find that $\lambda_\mathrm{Re}$ decreases for late-type Sc
and Sd spiral galaxies, with values than in occasions puts them in the
slow-rotator regime. While for some of them this can be explained by their
irregular morphologies and/or face-on configurations, others are edge-on
systems with no signs of significant dust obscuration. The latter are typically
at the low-mass end, but this does not explain their location in the classical
($V/\sigma$,$\varepsilon$) and ($\lambda_\mathrm{Re}$,$\varepsilon$) diagrams.
Our initial investigations, based on dynamical models, suggest that these are
dynamically hot disks, probably influenced by the observed important fraction
of dark matter within R$_\mathrm{e}$.
