A brown squirrel looks like a bump on a branch, and a green squirrel against the background of a brown trunk would stand out.
Stupid giraffe question: do giraffes ever sit or lie down? Becuase if they’re taking their ease on the ground, camouflage becomes much more pertinent.
To expand on the talapoins - they are rather similar to the vervet, sometimes referred to as the African green monkey, whose genus name, Chlorocebus, reinforces the notion. Again, it’s a matter of debate as to whether you would actually call them “green”:
Green? Well, maybe … sort of. 
<- Like this guy? No.
Can their major predators/prey even see colour?
I don’t know, maybe Colibri would know - I’m sure a major predator group would be raptors. I’m pretty sure most mammalian predators are colourblind, though.
Most mammals are dichromatic - their color perception approximates a human with dueteronopia, commonly called red/green colorblindness. There are other exceptions besides humans. Kangaroos have trichromatic vision, IIRC.
As yabob says, most mammals except for primates have poor color vision, with only two types of color receptors. Old World monkeys and apes including humans have three color receptors. Birds and most other vertebrates have even better color vision, since they usually have four receptors.
Don’t fight the hypothetical’s link has a fairly good discussion of reasons there are no really green mammals. As has already been pointed out, there are almost no other animals that are “really” green either, in the sense of having green pigments. Almost all blues and greens are structural colors. Mammalian hair may just not be suited to produce structural colors such as the ones that can be produced by feathers or bare skin. Also, since the vast majority of mammals are nocturnal, pattern is much more important than color itself.
As to the question in the OP, while it is difficult to know for sure, my own opinion is that bold patterns in animals that are mostly found in open country, like giraffes and zebras, are more likely to serve as interspecific social signals, or perhaps as “confusion patterns” for pursuing predators, than as camouflage. While in certain circumstances they can break up an animal’s shape, in my experience both zebras and giraffes can usually be seen very easily over great distances. This goes for giraffes even when they are standing in the midst of trees.
Stripes and spots on stealth/ambush hunters like tigers and leopards, that are often concealed in dense cover, are more likely have a camouflage function.
That is really cool - I had no idea that they existed. Any pictures of these purple cows? Apparently my google-fu is weak.
Dazzle camouflage or Razzle Dazzle – Dazzle camouflage - Wikipedia
No, it was one of my uncles who had it a loooong time ago. I’ve included some dope on Belgian Blues. It could have been one of these.
Of course such colors are man-made, so to speak, and probably wouldn’t occur in wild cattle.
Not that different from a Blue Duiker, though, a small African antelope.
As I was saying, such colors occur occasionaly in the wild. 
My MiL has one of these:
She firmly belives it came from a purple cow.
Oooh. Just thought of a possible exception to the rule – how about the bright rump/face displays of, say, a mandrill?
They’re as blue as blue can be.
On further googling, I found an abstract refering to “coherently scattering dermal collagen arrays” – so I guess it isn’t impossible to do that color scattering trick with skin, it’s just mostly animals haven’t gone that way.
Isn’t there a breed of dogs with very blue hair?
Plenty of birds and a few mammals like the mandrill have bright blue facial skin (or sometimes elsewhere, as in Vervet Monkeys , in which males have a red penis and a blue scrotum). It’s just that mammals are mostly covered with hair, which may not be as easy to modify to produce structural colors as feathers or bare skin.
You may be thinking of the Blue Tick Hound.
And we mustn’t forget chow dogs with their blue tongues.
Which brings us full circle back to giraffes…
There’s also the Kerry Blue though they’re only blue from a certain angle in a certain light.
Posts 34-39 have those animals that make me think “blue” must have been applied to them back in Ye Olde Days when we didn’t have to many color words, and this guy -> 
would be called “red”.
Blue dogs, cats, rats and tongues aren’t blue, they’re grey. I’ll grant the horse did have a bit of a blue cast, but I don’t trust photos - they’re too easy to color “correct” to a bluer hue if the developer so desires.
The primate privates, I’ll give you. Those are, indeed, a heck of a blue color!