So player in the group is picking up an Animal Companion, and I'm playing a Champion. I'm wondering does the animal have an alignment for the purpose of such Champion spells like Litany of Wrath. Does it go off the owner's alignment or is the animal considered neutral for all alignment effects?
It isn't specified. Since the companion has a "special bond" with its master, I think it's a safe bet to assume it has the same alignment, for any ability where it matters.
More and more, I'm simply ignoring alignment in my games, with the exception of clerics, champions and extra-planar beings and the like.
I don't know about Animal Companions in general, but the Champion feature Divine Ally specifies "Your devotion attracts a spirit of your deity's alignment" and then lists 'steed ally' as one kind of divine ally. So, not necessarily the same alignment as you, but close.
Because I do consider the Champion a little more divine aligned than the Ranger I'd say an animal companion is still more close to the original animal, which be default is (true) Neutral.
Having said so, there is absolutely no reason for an evil ranger to not have a mean, vicious dog (neutral evil) and for a good Ranger to not have a kind and benevolent dog (neutral good).
However as I don't think it's an automatic alignment match, I'd just say have player and GM determine the alignment once the animal companion is chosen and then roll with it.