I believe my cat knows when I'm sick without a doubt. I get terrible migraine headaches fairly often, and when I do I'm basically confined to bed - I have to make the room super dark, have no noise, and so forth. Now, my cat on a typical day is pretty hyperactive -- he's always running around the house, playing with our dog, and just generally causing mischief! However, on every single occasion that one of my horrible migraines has hit, he's been so calm and well behaved. He usually jumps onto my bed and just lays by my feet, as if to say "I'm here if you need company, but I know you're not feeling well so I am on my best behavior!"
He was also super caring and affectionate back when I was pregnant and had terrible morning sickness - so I absolutely believe they are aware when you're not feeling your best!