I keep strays! Every time!
I have two dogs of my own and I take them with me whenever I can even if it's just for a ride to bank. My most recent dog sitting experiences have been for a couple that vacations alot and has a pitbull/lab that loves being at home. The other was for a 90 year old woman that just returned from assisted living and wasn't sure she could walk her Golden Retriever the first week.