I have heard some reports that people tend to travel in multiples, especially internationally. Good for them - that might be interesting. Really, traveling alone has its advantages, but there are quite a few things to consider if you choose to just get away and haven't the patience to wait for someone to join you (or the tolerance for having them along).
Blend in, if you can.
In Malawi, I couldn't pull it off, but in Spain I could. Alone or with others, you are a target, but alone you are easier prey. Yes, you - the one with the great big backpack on your back and smaller pack on your chest. The only question is whether you will be a hard target or a soft target. There are plenty of people all around the world who thrive off of the misfortunes of tourists, and you need to prepare to minimize your risk. Be mindful of your clothing choices, so as not to stand out. Study the people and try to behave in a similar fashion. Remember, if you are running from the lion, you don't necessarily have to be faster than the lion, just faster than anyone with you. Tourists will stand out, and you may not be able to avoid it, just stand out less.
Preparation is key.
Of course, learn what you can about your destination ahead of the trip, but also use your protected time in the plane, train, or hotel to get your bearings so you don't have to break out the guide book or spend all your time on your smartphone out in public. I carry a small moleskine notebook in my pocket where I can put directions and notes; it's light enough to take everywhere and doesn't scream tourist.
Know your vulnerability.
Your first 24 hours in a new country or city are your most vulnerable. Try to have a flight that arrives in the daytime. Ports of arrival - airports, train stations, bus terminals - have people looking for travelers out of their element, and that's you. Arrange ahead of time how you will get to your hotel, and you will save yourself problems and frustrations. If an acquaintance can meet you there, even better. Otherwise, many of these places have information counters staffed with people whose job is to help you. While I can write a whole section on taxis, it's usually best to spend the money on a reputable service that can save you from walking the streets of a strange place alone with your luggage. Get a good grasp of the currency and what things should cost, because plenty of vendors will attempt to overcharge you. Also, once you are on your way in a new place, act like you have been there 50 times, so at least your apparent confidence makes you a harder target.
Talk to strangers?
Yes, your mother told you not to do that, and often it is good advice, but if you traveling solo, you will be very lonely, and you will miss out on much of what travel actually is. A good rule of thumb is be wary of strangers who come talk to you. Odds are if you choose the stranger, he/she is probably not a serial killer, and you might be surprised by some kindness and/or good advice. Also beware of anyone who asks you too many questions, and do not give out much personal information; feel free to make up some details if you want and have some fun with it. Often I will pretend not to speak English, which makes escape of nosey strangers easier.
Find your niche.
For me, it is restaurants. For you, it might be art museums. Go where you feel comfortable and have knowledge of your surroundings. This seems like a no-brainer, but use these places to get familiar with the new city and pick the brains of the people working there. It's like being part of a club, because these are your people, and having people in a foreign country is tremendously valuable.
This should be number one, but I am biased. Opportunities will likely only be available if you arrange ahead of time, and you should also take the time to properly vet an organization. Volunteering in a foreign land is one of the best experiences you can have in a new place. While you should do this because you actually want to help in some way, it can provide you with experiences you would have never found otherwise as a tourist. Also, you may make some great friends who are just excellent people.
Go to church.
Okay, obviously if you are not religious (or atheist) and not interested, this is not for you. However, many people have some connection to a religious institution. If that's you, take an hour on your given sabbath and check out the local service. You will likely be in a safe place, often historic and beautiful, surrounded by people trying to save their souls. Again, membership has it's privileges. Even if you are not a member, you are probably welcome and might even get some free coffee and cookies out of the deal. If you're lucky, they may ask you to read during the service and/or take you out to karaoke.
First of all, DO check in with a family member or friend from time to time; in case you do go missing, that makes it easier to track you down. DO tell your bank and credit card companies where you will be, so they don't cancel access to your money. DO register with your government or local consulate, in case of natural disaster or some other emergency. US citizens can easily register on the State Department website.
However, be careful how much information you put on the internet about your whereabouts. Do you really want a stranger to be able to look on Instagram and see in real time that you are an attractive woman on her third shot of tequila at your exact location?
Think when you drink.
Odds are, at home you have drinks with friends and at places you know. You know your risks there. In a foreign country, it's a different story.
Manage travel fatigue.
Odds are if you are in a foreign country by yourself, you don't mind a little down time and lack of conversation. Also, you enjoy wandering and discovering all that world travel has to offer. However, you may find that the stresses (and sometimes unfortunate circumstances) of long-term travel can add up after a few weeks alone. Don't feel like you have to be on the go all the time. If you are gone for a month, it's okay to go see a movie or drop in to McDonald's for an American coffee and a Sausage McMuffin. It's okay to take a day and just read by the river. Spend a little time with a change of pace doing something you enjoy, even if it's not something that that culture is known for.
Don't let any of the above dissuade you.
Maybe you have never traveled alone before, so the mere prospect seems a little daunting. If it's your first time, go somewhere you can speak the language. Go where you have studied or have some professional experience to which you can relate. If you can, go somewhere that you know someone - that doesn't mean you have to spend all your time with them, but it's great to have a contact. Go somewhere with a purpose, and the trip will all come together. Most places are scarier until you get there... and then you won't be able to imagine your life having never been.