Since this question gets asked a lot, I thought of starting a "helpful safety hints" thread for solo women travellers (kind of like the "helpful hints thread" in the general discussion topic). I’ve included the kind of common-sense safety precautions that people are frequently asking about.
1) Don’t panic. Europe is safe. Excessive paranoia will get you nowhere. 99.99% of the time, nothing will happen and you’ll be perfectly fine, so no need to overreact.
2) Wear a money belt. Under your clothes. Store your passport, some emergency cash, a spare credit card or bank card and any important documents in it. If your bag is stolen at least you won’t lose those.
3) If your hotel or hostel has a secure safe, lock up your passport and valuables there when you head out on the town.
4) Remember that everything is replaceable except you. If you get into a sticky situation, just hand it over. It’s not worth it.
5) You will probably stick out as a tourist, no matter how hard you try to "blend in". Just be aware that as a tourist, you may be a target of petty thieves, so keep your wits about you.
6) Never accept drinks from strangers unless you have personally witnessed them being poured. Don’t leave your drink unattended.
7) If you decide to get completely drunk and stumble home, or allow yourself to be picked up by some random guy, this isn’t a good idea but it’s up to you. Make sure at least someone you trust knows where you are and where you’re going. If you’re completely solo and don’t know anyone, conspicuously walk up to another woman in the bar and tell her loudly that you’re going with "this guy" – even if you don’t know her, the guy will think you do and he’ll think that someone is watching out for you.
8) Bring condoms with you if you’re even thinking about hooking up with someone – local or tourist. STDs are just as prominent abroad as at home. Be smart.
9) When in crowded areas like train stations, tourist sites, etcetera, wear your daypack in front.
10) On a night train, be careful of empty compartments where you’re the only woman, and try to get on early so you can share a compartment with other women. Make sure your valuables are safely stashed under your clothes in a money belt.
11) Remember that your passport is the most important document you have on you. Take precautions to make sure it’s not stolen.
12) Trust your instincts. If a certain area is making your skin crawl or your antenna quiver, don’t walk there alone at night.
13) When you arrive in a new city, ask the hostel staff or other travellers of good ideas for nightlife, and also ask them if there are any particular areas to avoid or things to watch out for.
14) Walk alertly, like you know where you’re going. If you need to pull out a map or consult a guidebook, duck into a shop or sit down at a cafe before doing so.
15) Unwanted male attention can happen anywhere. Your best bet is to just ignore it. If it’s persistent or it starts to scare you, walk quickly into a nearby restaurant, cafe, store or other place, or leave the bar if that’s where you are. Remember that 99% of the time, guys have no intentions more sinister than trying to pick you up.
16) Be subtly aware of your belongings even when you’re not paying complete attention. Loop your bag strap around you when you’re at an internet cafe or a restaurant. Keep your foot around it if you’re sleeping on a bus. Etcetera.
17) Again, don’t panic. These are just basic safety precautions but don’t spend all your time worrying about all the horrible things that could happen. Most people never have any problems whatsoever. Just have a good time, enjoy, and don’t worry so much.
Feel free to add yours!