I definitely feel that pets are in-tune to human emotions. My pets are snugglers, but with my dog especially I'm not always the first choice to go to for a snuggle. I don't stay still enough for him because I'm restless all the time. But I've been having some really hard times recently, and when I cry or feel sad he always comes over to me and stays by my side, and he gives me lots of kisses to try to cheer me up. My cat is the same. While the dog is often downstairs, my room is upstairs, and the cat prefers to sleep up here. When I start having a break down she's usually the first to notice, so she's the first to run over to me and curl up on my lap, purring and comforting me.
I think animals can also sense when a human is sick. When my mum had the flu a while back, the dog didn't leave her side for one moment. She stayed in bed for days, and he only left her side for meals and bathroom breaks. Other then that, he wanted to be there with her the whole time. He does the same when my illness gets particularly bad.