One of the biggest decisions facing any traveller, is whether or not to go alone. There are several factors to consider:

Benefits of traveling solo
Travelling solo does not necessarily mean you’ll be travelling alone for the whole trip. Quite the opposite, in fact. Most solo travellers, just end up traveling with different people for different legs of their journey. Single travellers attract single travellers. Plus, you’ll be approached by more locals. Which means solo travellers are much more likely to return home with an address book filled with contacts from all around the world.
Travelling alone is also a wonderful therapy for your character. You learn about yourself and, as people don’t know you, you can play with your personality by changing attitude every day. Last, you’ll be less distracted by a friend and more likely to notice the small things happening around you.
http://www.travellingalone.co.uk 
http://www.solotravel.org

Women alone
Women can and do travel solo throughout the World. Some countries and regions make this quite easy: Northern Europe, USA, Canada, Australia, New Zealand. As long as your wardrobe is conservative, you’ll often be afforded the same status as male travellers in most developing countries you visit, but expect numerous enquiries. For this, always trust your instinct.  Check also websites specialized on this target.
http://www.women-on-the-road.com

Travel with others
There are obvious benefits to travelling with a companion: medical security; money saving by staying in double rooms or sharing a taxi. But also: minimising travel shock, having moral support, share a meal, not being bothered by some garrulous local.
If you decide to go with another person, check if your budgets are in alignment. Also, give yourself the option of separating for a while; just a morning or afternoon each day, or a week or two along the way.