When you travel alone, especially as a woman, you unfortunately do need to look at the world a bit differently. Decide how 'safe' a country or area is, then plan accordingly. It also might make a difference as to whether you have a car or not.
Probably the most important thing I can say here is to use your best judgment. If a situation doesn't feel right, for whatever reason, don't do it. This advice holds true for in your own home country as well as overseas.
An example: I was in my early 20's traveling through Europe with some friends. I often had days to myself though when I wanted to do something different than the rest of the group. On this particular day, I had read about a bunch of ruins, so I set out walking while my friends went to sunbathe on the beach. The ruins lay beyond the edge of the small town. As I walked, I noticed a man who kept riding back and forth on his bike... slowly... looking at me. When I reached the edge of the town, I saw that the path led through some tall, remote fields. I could see the man circling back again in the far distance. So I decided to skip the ruins and stay within the safety of other people. Sure, I was disappointed, but I felt the potential risk just wasn't worth it.
If you are uncomfortable with traveling alone, here are some options:
1) BE FLEXIBLE TO OPPORTUNITIES
Sometimes my trips are determined by who else can go with me, or if I have a friend living somewhere to visit. In 2005, I was all set to go to Peru by myself. However, I learned that a friend had moved to Thailand. I wrote a few emails and presto... I was headed over to Asia and had my own personal tour guide. In 2008, a good friend called me and asked if I wanted to join her in rafting the Grand Canyon that summer. It hadn't been on my list, but I quickly rearranged things so that it was! And remember, the more you talk to your friends about your dreams and the things you want to do, the more you will pop into their minds first when they are thinking about who to invite along.
2) TOURS (single day or extended)
In general I don't do complete package tours, but I did use one to China and had a lovely time and made some lasting friends. Mostly what I enjoy are day tours (or two- or three-day tours). These are convenient ways to cover a lot of ground and get to areas that might otherwise be impossible. These are particularly great for doing adventure tours, where all of the gear is supplied for you. An example of a day tour I had in Thailand: We first visited a snake farm (where I got to kiss one of the slithery creatures for good luck), then got a short elephant ride to a river where a local took us on a tranquil raft ride downstream, and finally we were picked up by an ox-cart and brought back to the bus. It was great! And there would have been no way for me to have arranged all that by myself.
3) MEET PEOPLE ALONG THE WAY
This is easy to do, especially when you are staying in hostels or camping. I often meet someone or a couple that I connect with. We will spend a lovely day together seeing things, then go our own ways the next day. Couchsurfing is also good for this. People frequently enjoy showing you where they live. I myself have done it for those who have stayed with me.
4) WOMEN ONLY
If you feel more comfortable being around other women, look for women-only places to stay. Often hostels will have at least one dorm room dedicated only to women. There are probably also many clubs or groups you you can find as well who might be able to offer support.
5) READ REVIEWS
Sometimes you have to take other people's comments with a grain of salt, but on-line reviews of either a country, accommodation, tour, or whatever it is that you are researching, can be quite helpful. Again, use your intuition, and if something doesn't sit quite right, walk away. Undoubtably something even better will show up! Also, get recommendations from friends.