Why are my followers trying to murder me?
Solution 1:
One possible explanation may be the fact that if you are a vampire in the final stages of the disease, everyone will begin to attack you on sight, even your companions, due to their fear of vampirism.
Solution 2:
There are some reports that Delphine's AI is buggy and will cause her to randomly turn hostile, but UESP says that she will be hostile if you have a bounty on your head, so it may not be all that random or buggy after all.
Solution 3:
You probably have a high bounty for something. This happened to me when I had Farkas as a follower. He was all glitched out so I went to Falkreath and let the guards read me the riot act, paid my bounty, and Farkas acted normal again.
Solution 4:
Happened to me with my follower. I used Voice of the Imperial which made her stop attacking, but then she also left my service. Then I just had to ask her to follow me again and everything was fine. Yay.
Solution 5:
It happened to me as well. Fast travel to another city, and then wait 48 hours (buy a room or use wait mode). After that, she will be fine with you.