If you do keep sheep and goats together, keep in mind that goats need copper and copper is bad for sheep. You will have to find some way to supplement the goats. You could do this by feeding them separately, providing a mineral supplement specifically for the goats, or copper bolusing (sp?). Even if you don't have sheep, I recommend copper bolusing. It helps them fight parasites and gives them a nice shiny coat. Other than that it seems like they have very similar requirements.
I have also heard of keeping a donkey with goats as a livestock guardian so I would imagine they get along fine. Same thing with llamas/alpacas.
I know you are asking about larger animals but I have successfully kept different types of fowl together that most people would recommend against with no issues. My peafowl lived with my ducks until they were old
enough to free range. Now my peacock is protective of the ducks. I also kept some
chickens and ducks together until their coop was finished. I think all three were together at one point. They were all very young when we put them together and they had plenty of space so they never fought with each other. I guess my point is that, I believe if you get any animals together young enough, they will bond or at least tolerate each other. When those animals start having babies, the older ones leave them alone because they don't see them as foreign.
Another thing to consider, if you are setting up a paddock system, you can always keep them in separate paddocks. Let the goats and sheep through one paddock first, then follow with the hogs so they don't get the good stuff first. Then follow them with the
chickens who will scratch and break up any droppings and till into the soil.