My recently adopted podenca Rosely (Rosie) is my shadow. Which is great to a certain extent, but not good when left. I've never had a dog with separation anxiety problem, probably because most of my dogs have had companions. However, when Rosie first arrived, she did not have a housemate, so we had the howling and door scratching when left at night. I've never allowed dogs in bedrooms but now we're in a bungalow, I've given in and Rosie has a bed at the side of mine for overnight sleeps.
I do a couple of mornings voluntary work with Riding for the Disabled and also an animal charity shop. On both occasions she showed serious signs of distress - luckily my other half was at home with her.
Her new housemate blind Podenco Bo arrived a week later and so over the weeks during the 3 months she has now been with us, she has adjusted to being left with him, although my other half says she sits at the patio doors looking for me. The greeting I get on my return home is wonderful, I must say.
So I'm slowly working on her separation anxiety but can now appreciate what a problem it must be for those people who are not able to have more than one dog.
Here's a link to an article by the Royal Society for Prevention of Cruelty to Animals, the UK based animal rescue charity.