Absolutely, whenever I was feeling sick or sad about something, my coonhound wouldn't leave me alone. She would follow me from room to room and lay next to me the whole time. Sometimes she would just stand there staring into my face while I was laying down.
One time, and the only time she ever did this, she nipped my finger when I was trying to get her off of our bed. If it was anyone else she would have taken their hand off completely, because she did not like to get picked up at all - I was the only one she would let pick her up. She was stubborn too though and wouldn't move if she was comfortable somewhere. Anyhow, I gave her the cold shoulder the whole next day and didn't pet her or acknowledge her or anything. She kept following me around the house and wimpering because she didn't understand why I was ignoring her, lol.