Between working at a job where I see a shit-ton of violent crime and reading umpty-billion Internet posts on rape, sometimes I feel a little overprotective. Like I have to be on my guard against men who show any sexual interest, because being attracted to a woman is basically a threat against her. A guy I don't know just up and looked at me? AAUUUGH MACE AND RUN.
But no. Sometimes a "hey there" really is just a "heeyyyyy there." Sometimes it's flattering, even empowering. There really is such a thing as a Friendly Ogle. These are the qualifiers for staring at a strange woman and being uncreepy, the Gentleman's Guide to Ogling:
1) Keep a neutral or happy expression on your face. Scowling and ogling is mega-creepy.
2) If she looks back and "catches" you, be friendly--make eye contact and smile, or even wave or say hi. Then leave it at that (and stop ogling) unless she decides to extend the contact.
3) No touchy. EVER. Even a little, even on somewhere totally neutral. Personally I don't think even tapping someone on the shoulder without their permission is ever okay, but if you are the sort of person who does that, at least don't do it to anyone you're thinking about sexually.
4) Only ogle from a reasonable distance; don't loom. Don't ogle in an elevator or narrow passageway or somewhere else where she's stuck with you.
5) Talk to her like she's people. Guys who say "I'm sorry, I just was noticing that you're very pretty" get laid sometimes that way, or at least get treated nicely; guys who go "whoooo hot mama!" I'm pretty sure do not ever. (I think these guys don't really want or expect the woman to react positively, so I don't really know what the fuck they are thinking, other than "I'd like to make it a little more difficult for her to walk down the fucking street.")
6) Even if she doesn't seem to have noticed you, restrain your ogling time to a reasonable once-over, not an unbreakable Death Stare.
7) If she scowls or curses at you, even if you were being totally nice and nonthreatening, just let it go. She didn't agree to this interaction, so she doesn't owe you politeness. Explaining how you were just paying her a compliment, geez is never helpful. (And I don't think I have to point out that the "you think I was looking at you? don't flatter yourself" denial is all kinds of fucked up.)
So yeah. It's okay to be attracted to women. It's okay to hit on them and even ogle them. If you're respectful and friendly and treat them like people, it's just fine by this Humorless Feminist if you stare at total strangers in the street. You have my permission.