Does animals have feelings?

Just a quick thought.. I just thought about, you know, when people say that animals don't have emotions, or 'it's just a cow', or whatever..
 - I just thought about, that the moments I, a human, feel most emotional, have the deepest feelings, feel more alive, is when I do things that most animals/mammals also do - Make love, give birth, breastfeed, staying in nature or with close family.

It is not when I am solving math, or dressing in human clothes or eating my food with a fork or whatever we humans do.

So it's a funny thought really.. that so many people think that emotions and feelings come with intellect,
and not just by being a part of nature....