THE SIMPLE ANSWER: I DON'T INTENTIONALLY CARRY A WEAPON TO PROTECT MYSELF FROM POTENTIALLY DANGEROUS PEOPLE. BUT...
As a woman, the fear of something truly horrible happening (e.g. getting raped) is definitely a consideration when going backpacking, or more accurately, in life. Maybe it's not rape, maybe it's just getting harassed by some heebie-jeebie dude(s). Regardless of whatever scenarios might be playing out in your head, it's probably safe to say these thoughts probably cross the minds of most women, even if just for a brief moment. I certainly have played out harassment scenarios in my head, even when I'm in the middle of nowhere and haven't seen a soul ALL DAY!
All that to say, I have definitely considered carrying some kind of weapon, but hadn't until just a year ago when I started carrying a pocket knife. My primary reason for carrying it isn't to use as a weapon though. (I would be terribly slow at getting it out and flipping it open; and it would be hardly intimidating!) The main reason is to have one in case of a serious emergency (or if I feel like whittling a piece of wood). For real though, I carry it for the same reason I carry a lot of extra first aid materials. After getting Wilderness-EMT certified, I now know how to use all the extra things I take and want to have it available in case it might save someone's life. This includes the knife. (Before, I didn't even feel comfortable opening my pocket knife!)
But back to the fear of dangerous people. I think that fear can be especially strong when you consider being out in the wilderness, out of reach from civilization. I mean...."what if something happens and there's no one around?!?"
The key phrase here is being "out of reach from civilization." Did you catch that? It seems that most of the bad things happen when you're actually surrounded by people in civilization. It's highly unlikely that some dangerous person is lurking out in the wilderness waiting for you. (That'd be a lot of food to pack in!)
Most people on the trail are there for the same reasons you are: to get away from daily routines and the noise of the city and to get nourished by being in the wilderness. Haha, actually, I find that people can definitely be amazingly friendly on the trail, but they usually want to avoid people. :-)
If it gives you a sense of security to take pepper spray, take it for the first few times you go in the wilderness. Once you get more experience, I have a feeling you'll likely start leaving it at home. But girl, do what you gotta do. There is nooooo judgement.
On a side note: In bear country, I absolutely carry bear spray with me. You sure can use that on any dangerous folk if they're coming after you, but since that's an unlikely scenario, I'd save it for the bears!
Hope this helps!
PS. If you're curious about some statistics about rape, I found a helpful infographic here.