  We report the detection of far-infrared (FIR) CO rotational emission from
nearby active galactic nuclei (AGN) and starburst galaxies, as well as several
merging systems and Ultra-Luminous Infrared Galaxies (ULIRGs). Using
Herschel-PACS, we have detected transitions in the J$_{upp}$ = 14 - 20 range
($\lambda \sim$ 130 - 185 $\mu$m, $\nu \sim$ 1612 - 2300 GHz) with upper limits
on (and in two cases, detections of) CO line fluxes up to J$_{upp}$ = 30. The
PACS CO data obtained here provide the first well-sampled FIR extragalactic CO
SLEDs for this range, and will be an essential reference for future high
redshift studies. We find a large range in the overall SLED shape, even amongst
galaxies of similar type, demonstrating the uncertainties in relying solely on
high-J CO diagnostics to characterize the excitation source of a galaxy.
  Combining our data with low-J line intensities taken from the literature, we
present a CO ratio-ratio diagram and discuss its potential diagnostic value in
distinguishing excitation sources and physical properties of the molecular gas.
The position of a galaxy on such a diagram is less a signature of its
excitation mechanism, than an indicator of the presence (or absence) of warm,
dense molecular gas. We then quantitatively analyze the CO emission from a
subset of the detected sources with Large Velocity Gradient (LVG) radiative
transfer models to fit the CO SLEDs. Using both single-component and
two-component LVG models to fit the kinetic temperature, velocity gradient,
number density and column density of the gas, we derive the molecular gas mass
and the corresponding CO-to-H$_2$ conversion factor, $\alpha_{CO}$, for each
respective source. For the ULIRGs we find $\alpha$ values in the canonical
range 0.4 - 5 M$_\odot$/(K kms$^{-1}$pc$^2$), while for the other objects,
$\alpha$ varies between 0.2 and 14.} Finally, we compare our best-fit LVG model
..
