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, $ u 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 ..
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