We recently picked up a medium to large 5-year-old Rottweiler, and she is very well behaved. Rarely barks, loves to cuddle, quiet, timid, knows release, heel, and sit. When handing her treats she gently takes it from your hand. She isn't protective of toys or food either. She also walks next to me when I take her for walks.
She loves to play with my Jack Russel who is a little over one year old, and she "tolerates" my male cat. When it comes to my female Blue Russian cat though, she will stare. and stare. and stare. My Rottweiler could be laying on the bed, and the cat in the other room. She will sit on the bed for literally hours and not move. Just staring at the cat. She will not react to commands. The only way to break the focus is to close the door or literally grab her and pull her closer to us.
When both animals are near each other, be it on the bed or elsewhere in the house, she will tower over the cat and look down just staring at her. In this case though her focus breaks when the cat meows. Then she'll move, lay down, and just whine. We aren't sure if this is her looking for the alpha female or what.
Edit: last night she stood over my cat while staring at her, but her tail was wagging. Once my cat meowed, she laid down and whined for a short period. She does not show any sign of aggression. It seems more like she wants to sniff the cat, but the cat doesnt let her so she simply stares at her.