I have brought my cats to work with me when they needed to see the vet for something, or get vaccinated etc... Recently I was filling in for the receptionist when she was sick and I had brought one of my kittens (about 8 months old) for vaccinations. Everyone who came in thought it was cool how she was just sitting on a chair and relaxing behind the reception desk while she was there. My littermate kittens are SO laid back! I've taken them to my friend's pet boutique a few times to see their sister (she adopted one of the littermates as a 'store cat') and they just hang out calmly, don't even mind her dogs running around them.
So far I haven't brought my dog Bianca to work for the day because she is not always good around other dogs (we're working on that) when on a leash and so when she needed to see the vet I had a family member driving me to work with her on a day when there were no appointments until later in the morning, and had them wait while the vet treated her and then drive her back home.
I also do petsitting and usually if I am petsitting for someone in my neighborhood with dogs, when I give them their daily walk I would walk my dogs and the dog(s) I am petsitting together. When I walk my dogs I usually have a family member come along and we go 2-3 miles usually so that way the dog(s) I'm petsitting get the benefit of a nice long walk too and since there are two people it's not a problem having an extra dog along.
I brought my dog Ginger to my university a few times but not for classes obviously. It was usually because someone wanted to meet her so I brought her when I didn't have classes. There used to be a woman who worked there who had a service dog who was a red-colored Golden Retriever, he looked like he could've been Ginger's twin when Ginger was younger. When I first met him I did a double take because it looked like she had my dog!
She wanted to meet Ginger so I brought her to her office one day. Ginger and Casey (the service dog) got to play together and had a lot of fun!
Here's a photo: