Women can travel and do travel, and many do it solo. Most travel tips apply as much to women as they do to men, but there are some aspects of travel in which women need to exercise more care than men (there are also some in which women are, sometimes surprisingly, safer). The specific travel tips for women depend on where and when and how you are travelling, but many general rules apply everywhere.
(1) Don't let the fear stop you from exploring and getting out of your comfort zone. Although women travelers are vulnerable to some dangers, they are safer from others. Follow your instincts, but not your prejudices. In most cases, things will turn out fine.
(2) Enjoy the opportunities for interaction that being a woman can give. In many societies, male strangers will not be able to talk to women, especially married women, socially. As a woman, you may gain insights into the life of local women and families that are completely hidden from men.
(3) Exercise similar caution you would at home. This is perhaps the most important tip – and rule – that applies to all travel, be it a two-week package tour or a six-month backpacking trip. The general rules of safety, be it in the street, in a bar or on a train don't change just because you are abroad.
(4) Learn something of a local language. This doesn't need to be much (although generally, the more the better), but even a few words always help. Particularly in any kind of emergency, if you can ask for help somebody that doesn't speak English, it may make all the difference.
(5) Learn something of a local culture. Rules of behaviour, and of what is appropriate for men and women, differ between cultures and countries. You rarely have to respect all the local rules, but it often pays to do so. In many countries, a woman travelling alone is an oddity. In many cultures, behaviour that is normal in Europe or US will be seen as provocative. To avoid sexual innuendo, harassment and unwanted advances, cover up if this is a local custom (particularly useful in Muslim countries), avoid direct eye contact and if you can, try to interact with women rather than men. Take cues as to appropriate behaviour and dress from local women. On the other hand, certain behaviours or attitudes that are offensive to American or Western European women, are normal in other countries. Withhold judgement and don't assume your values and attitudes are necessarily better (and even if they are, keep quiet until you know your opinion is sought after).
(6) Invent a husband or a fiance. Although it might seem hypocritical, an imaginary husband or a fiance is a very useful thing (even as far as a fake ring). Many men in foreign places will be much less likely to harass you if you say that you are betrothed to somebody.
(7) Be careful about holiday romance. Holiday romance, either with a local or a fellow traveller, is for many an essential part of the travelling experience. But as in tip 1, remember to take precautions (sex on the beach is not automatically safe sex) and try to avoid predatory and mercenary encounters. Always carry condoms (unless you are absolutely certain you would stay celibate), and if you can, have emergency contraception or information on how it can be obtained with you.
(8) Appear confident but not cocky. Walk purposefully, stand tall, and know where you are going. If followed or harassed, appeal to a local, ideally an older woman or a family group. This is more likely to work if your dress is not overtly provocative, but is always worth doing.
(9) Don't carry a handbag (use a money belt or a neck wallet), but always have enough cash on you to be able to afford to get a cab or use a telephone in case you get caught out late in a less savoury area.
(10) Don't be afraid to ask for help or assistance. In many countries, a woman travelling alone, especially a young one, will be naturally taken under wings of older women or families. Use this willingness to help (but know when to cut the strings too) both for safety and insight into the local society.