I've had all sorts. Easiest is the one who is aboard and promptly moves when asked. Worst is the long term squatter who is just looking for a place for their boat. I had one squatter on a winter mooring (no pickup or pennant, no safe chain) where I had to go to the harbor master/police to get him evicted. He ended up on an anchor, then on a private beach. Pay loader put the boat onto a flatbed and away it went. Hasn't been back.
Best solution (particularly for destination moorings) is to make them hard to pick up. Definitely no pennant and no large eye to pass a mooring line. Friend has a mooring in Breton Cove that I have permission to use - top of mooring is a stainless bar with a 1/2" hole. I drop off in the dingy with a pennant having a suitable shackle while the Admiral makes a circle. When she returns, the mooring is ready.
With my club mooring, I have yet to find someone on it when I returned from sailing. If I did, first call would be to the launch operator. What's up? I'd probably just remove the intruder from my pennant then tie him off my stern.
One time I pick up a mooring at Fishers Island (the wrong mooring). The owner returned while I was aboard, and insisted that I not move. He just tied up off my stern and asked me to put him onto the mooring when we left.
So, there are all sorts of situations regarding moorings. You just have to do what you're comfortable with and take what safeguards you can with what's yours.