I was born and brought up with my family in a protective setup. I had hardly lived out of my home except for very short durations. So when I expressed my desire to undertake a solo trip, my friends and family were obviously a little worried and thought I was joking. Then as they realised I was serious about it; the usual concerns followed: "Would it be safe?" "Aren't you scared?" "Would any of your friends join you?" "How will you move around on your own?" Almost all the so-called progressive and forward thinking people around me questioned my decision and in turn my ability to accomplish the task. I went ahead and embarked on the journey which paved the way for zillions of trips to follow and most importantly taught me a lot of things.
I learnt that the world isn't a scary place; but when you are on your own you are extra cautious, you trust your instincts, you are independent and responsible for your own safety. So as long as you plan ahead and act responsibly, you can be as safe alone as with any large group. It does help to read and research as much as possible about the place and travel & options. Booking the major travels and accommodation before hand is a good way to go about for a solo trip.
Just because you travel solo does not mean you would end up being lonely during the trip. Traveling alone provides you the opportunity to interact with new people, make new friends, gel with the locals and many times you end up meeting awesome fellow travelers.
Many women feel that eating alone in a restaurant or having a drink alone catches everyone's eyes and is embarrassing or unsafe. It isn't. No one really cares if you sit and eat alone and you might end up meeting some co-travellers which are fun to hang out with' but be a little alert before completely trusting a stranger.
It is better to travel alone than to tag along with someone (just for the sake of having some company); because it is possible you might not find a like-minded companion. Choosing the wrong co-traveler would wreck your entire trip and hold you back from doing a lot of fun things you would rather do. So erase the conception that traveling with any random person is better than traveling alone.
Traveling solo will teach you a lot of things about yourself; will make you try a lot of things; your uninhibited side would surface; you would explore and witness some incredible things and bring back tons of priceless memories.
Just ensure to be street smart, be proactive in using public transportation, carry some sort of self-defense or safety tools, be culturally sensitive to the locals, carry all the necessary documentation that may be required and always trust your instincts.