I've edited one or two of the responses for length, but I left the content as is. You'll see some repeats, but I kept them in since I thought that emphasized how important the tip was, and also because each person had a slightly different, useful take on the idea. Also, since were are talking about sex-specific advice, a few of these things are going below the belt, so if you're squeamish or easily embarrassed by those sort of things... well, I guess you've been warned.
So, in no particular order, here we go:
1. Remember that while verbal harassment is annoying, it is not necessarily indicative of any actual threat. I had really obscene things shouted at me in India, but I don't think I was ever in any danger (besides from microbes) It's not to say that it's pleasant or you want to put yourself in those situations, but don't add to the unpleasantness by scaring yourself unnecessarily. Many countries are safer - even for women - than the US.
2 Dress appropriately. You will get less unwanted attention (or at least politer attention) if you dress according to the norms of the country. In India for about 7 bucks I bought two sarwal kamis - the very long shirt and pants and shawl. No one was inappropriate towards me in all of my stay in southern India (the north is a different story). The shawl was also nice because it could double as a head cover - either for sun protection or modesty.
3. Look into menstrual cups so you don't have to worry about carrying/ finding your brand of tampons/pads. (They're more environmentally friendly too!)
4. For the 3rd world (and parts of the more developed world): learn how to pee without actually sitting on the seat. If you don't do this before you leave, you'll learn quick. Holding it until you get to a clean toilet is not an option. It's mostly a matter of strengthening your quad muscles.
5. This isn't particularly for women except I think they tend to be lighter sleepers: EAR PLUGS
6. Bring a sarong, it's useful as a skirt, a beach dress, shawl, head cover, an extra blanket, something to change behind/under when privacy is lacking
7. In many countries it's more appropriate for you to approach a woman to ask for help/ directions/ etc... Unfortunately they are less likely to speak English, so it's a bit of a trade off. (Note from Joel: I found in many Latin American countries that women were better for me to ask for directions because they'd to admit it if they didn't know where something was. Some men in cultures where machismo is a big deal would rather point you in the wrong direction than admit not knowing how to get there.)
I think it is interesting to note the difference between solo female travel and female travel with other people. A solo female has a lot more to worry about since she must make her way through foreign lands with an eye out for her own safety.
1) Female travelers (especially solo ones) simply need a little extra $$$. They must have a bit extra money to avoid potentially uncomfortable and dangerous situations as hitch-hiking solo, staying with strangers, to avoid staying in a crummy guesthouse where you simply don't feel safe, taking a taxi at night instead of walking...the little things.
2) Don't put yourself in a situation where you end up being alone in the front seat of a taxi, especially at night. If sharing a cab with other guys, have them drop you off first at your destination. If you must be alone with a cab driver, move to the back seat and don't start overly friendly conversation (esp. at night). Also, make sure the cab driver knows where he's going but don't assume that he does even if he nods and says yes 5 times. Give him/her an address and map and be conscious of the surroundings outside your window.
2) Fake wedding rings...I have one, but haven't really used it. But good to have if you feel it would make a difference in safety in different situations or places. Could steer the creepy older men at the bar away from the younger female backpacker prey. Also good for checking in at cheap hotels so the wrong people don't get the wrong idea.
3) Dress appropriately. COVER UP IN CONSERVATIVE CULTURES. There have been numerous times when I wanted to scream this at other girls sporting midriffs and hot pants and watch as the entire block of local men step out of their shops to stare. Not only does it perpetuate the stereotype that Western woman are easy and sleep around but can bring the wrong advances from not so nice local men.
But ok, it's HOT outside, so stock up on linen and silk clothes before you travel. I have a white silk scarf that I use to cover my shoulders and doesn't add any extra heat in hot weather. When you get to a local culture buy cheap clothes that the locals wear such as long breezy skirts, lightweight pants, etc. Also, in conservative cultures, wear a more conservative swimsuit to the beach. If done right, you shouldn't need to sacrifice style to stay cool and dress appropriately.
4) Stock up on tampons (preferably the mini ones that fit into the palm of your hand) before leaving home, especially in Asia where they're almost non-existent.
5) After sunset, don't walk by yourself and talk on a cellphone while you walk. Stop walking to receive a call or make a call and resume walking after hanging up. A distracted female is a better target for mugging. Unfortunately this is another one from personal experience but I wasn't mugged, my cellphone was stolen from my hand while I was talking on it and walking. It can happen, so be alert.
6) In hotel rooms, deadbolt doors at night.
7) If you are caught in a situation walking alone at night, walk confidently, look people in the eye, and be aware of your surroundings to make yourself seem less vulnerable.
I think my biggest advice is that with a bit of confidence, some awareness of surroundings, and a lot of common sense, traveling can be great for single women. I think there is a lot of fear about traveling solo for women, and some of it is justifiable and some of it is not, but overall just having some safe practices will take care of you.
The first thing I'd say is know the country you're in and what the views on women are. Many cultures may see a single woman traveling as reflective not just on her morals but her families - how could your brother/father/husband let you go out on your own!! In other circumstances, it may be just fine that you're traveling alone, but you'll have to deal with cat calls. The bottom line is that almost all countries agree that there is a line where harrassing a woman is absolutely deplorable/despicable. Before going anywhere, try to understand their views on women, and use that knowledge to your advantage. For example, when I rode a bus alone in one culture that believed that one of my male relatives ought to be by my side, I made sure to sit next to an older man and I think his paternal side gave me protection from the cat calls I was receiving from younger men earlier. Sometimes its as easy as wearing a [fake?] wedding ring. Whatever situations you are in that might be less comfortable, if you know the culture's views on women, it will make navigating them more tolerable.
Dress appropriately. I can't stress this enough. Whatever the women of that culture wear, at best try to match the conservative level. I understand there are issues with women's rights and you may want to take a stand against having to cover your head or wearing a burka because you may believe that is wrong. Fine, but know that in doing so you have made a choice to bring on other possible consequences. I'm not saying fighting for equality isn't a good fight, but there are more effective and efficient ways to do that then being a solo foreigner dressing liberally in a conservative culture. At very least, in most cultures, be aware of the amount of leg, cleavage, and neckline that they show, and try to match (if not be more conservative than) what they do.
Figure out a hair style that you can manage without much equipment. I've heard from some that super short hair is the way to go, others that have gone long hair and pony tails. I have traveled both ways, and for myself I felt that, if I could shower nearly daily, then both are manageable hair styles, but that pony tails are better when you're doing more camping and shower-less travels. If you can manage to travel without a blow dryer, do so. Any time you want to look nice/fancy, you will be able to either (1) stay in a nice hotel for a night and use theirs, or (2) borrow one from a fellow hostel stayer. Definitely suppress the urge to bring other tools like a straighter or curling iron.
Plan outfits. With clever shopping, you can find a pair of sandals that function as both comfortable walking-around sandals and nice for a skirt and a fancy night out. Ditto on shirts, ditto on pants, ditto on the whole shebang. The big thing is think through everything you probably will do on the trip. For me, I conceptualize on how often I will want to be athletic, fancy, "normal", in hot weather, and in cold weather. Then once you figure out this list, find as many articles of clothing that cross these boundaries - like a plain white t-shirt that can be for athletic and normal wear but with a skirt could also pass for fancy. This keeps the load small while letting you be a girl - somewhat - about fashion.
If you want to go out at night, or are more of a party girl, and are traveling completely solo, then make a point to befriend someone at your hostel and go out with them.
PS. There's also a really cool but intimidating invention I think called Rapex that a woman can wear inside her so that, if she is raped, it clamps down on the man so she has time to get away and leaves the rapist in need of medical attention. Random fun fact for you.
And there we have it! Special thanks to all three backpackers for helping out! I should also note that Sonja told me she'd be happy to help out girls with specific questions, so if you have any questions for her, I can forward them on. If you've got something specific for Sonia or Emily, no promises, but I just might able to browbeat them into answering a question or two themselves.
I highly encourage any other women with independent travel experience who want to share tips to comment on this post. If you have any problems with that, you can always email me instead, and I can post your message.