Definitely. Bad days aside, they would be depressed over the loss of a companion or their kid or when some one from the family is not around.
Whenever I goes on a holiday, my pet would mopped around, hardly eat and drink and leave her toilet business to the last hour of the day. It was always depressing for me whenever I called from overseas to check on her and got all this feedback.
Same with my other cat who's closer to my Mum. Whenever my Mum is away, she would show the same symptons PLUS crying loudly from room to room.
I'm one of the caregivers for the strays and noticed that whenever a kitten goes missing, the mummy will become very lethargic if she can't find her kid after searching for a few days.
Yes, cats do get depressed.