Important question

Q: How can you be traveling alone, isn't that not allowed in your religion or something?

I can't tell you how many times Ive gotten this question from Muslims and non-Muslims. And to be honest, Im quite tired of answering it again and again, so Im writing it down for reference.

Short answer: It is permissible for Muslim woman of any responsible age to travel alone.

Long answer: (warning: this is a technical answer)
Point 1:
Islam is based on your intentions as well as your actions. You can not have sound intentions, but knowingly do wrong actions, and you always have to have pure intentions for anything that you might do. If you have good and pure intentions for something, but the act leads to a negative consequence, even though you tried your best, then you learn from it and try not to repeat it. If you have good intentions and your action turns out good, then you are rewarded. If you have bad intentions and go about doing a bad action, then you are negatively rewarded for it. If you have bad intentions, but something good comes out of it, even though you tried to do bad, then you will be rewarded for the action and not the intention. Therefore, it is important to always have sincere intentions in everything we do, not only religious acts of worship, but every movement. It is a way to remind ourselves of the fact that we are here to worship.
If you are Muslim, you will most probably already know this. This was related as Imam Al Nawawi's first hadeeth of the 40 most important hadeeths (sayings) by the Prophet Muhammad (pbuh). Please see Hadeeth 1 on this website: http://www.livingislam.org/n/intn_e.html
Are you still with me?
Ok cool.

Point 2:
A human being is created to worship God. (Quran 51:56 "And I did not create the jinn and mankind except to worship Me.") There is absolutely no other reason to be here. A woman was not created to give birth to children. A woman was not created to complete a man. There is only one purpose for every human being and that is to worship God. Worship comes in many different forms. In every act we do, there should be an element of worship. If a woman chooses to educate herself by going to university, there is worship in that. If a woman chooses to raise children, there is worship in that. We were created to worship. And we were given a brain to make choices.

Point 3:
Men and women are equal in front of God. (Quran 3:195 "I shall not lose sight of the labor of any of you who labors in My way, be it man or woman; each of you is equal to the other"). There is no difference between a man and a woman in front of God in terms of actions and deeds and worship. If there is a physiological difference, then that is only intended for the reasons of potential procreation here in this life (in this dunya). In reasoning, spiritual, religious, responsibility, accountability, and all aspects of life, there is no difference. The fact that purely cultural traditions have inflicted horrendous breaches of inequality - (dis)honour killings, forced marriages, prescribed dress codes - does not mean that these things have anything to do with Islam. Please get to know the difference between embedded cultural traditions which differ (in good and bad) from each region to region, and the true definitions of Islam.

Point 4:
The Prophet, peace be upon him, gave the good news that women will one day be able to travel alone:

Adeey b. Hâtim narrated:
I was beside to the Messenger of Allah. A man came and complained for his poverty. Later, another one came and complained for the bandits that waylaid people in order to rub them. The Messenger of Allah said:
- “Adeey, have you seen Heerah?”
- No. I have not seen, but I heard about it.
- “If you would live long enoungh, you will see a woman, inside her strongbox over the camel, traveling from Heerah at Ka’ba for pilgrimage, without fearing from anything, except Allah.” He said.
I was surprised and I said to myself: “What with the bandits of Tai tribe, those who fired the sedition and mischief all over the towns?…
Adeey continued his words: I saw the woman traveling from Heereh and walking around Ka’ba, without fearing from anyone, except Allah. (Bukhari, Stories, 25)

(Heereh: İt is a town established over a meadow near Euphrate, in the South-East of Kinidre, which is 5 km in South of Kufe, between Kufe and Havernak, today related to the province of Nejaf in İraq.)

In this hadeeth, the Prophet was claiming that there will come a time when women will be able to travel alone and safely without fear of anything or anyone but God.

Point 5:
There is a concept in Islam called Ijtihad. It is when Islamic rulings, those that are neither in the realm of halal (permissible) or haram (forbidden), and those that are not prescribed rituals, are studied in their current context by knowledgeable scholars. The issue of Muslim women traveling alone has been regarded by many knowledgeable and modern day scholars who have permitted the traveling of women alone, given that her safety will be taken into consideration. These new rulings were given in many fatwas which can be found online. For example: Sheikh Yusuf Al Qaradawi, a prominent Islamic scholar, said the following:
"If security is guaranteed and fear is no more present, a woman may travel, particularly nowadays when travel has become easy, whether by air, train or coach. In all these means of transportation, company is available and security is realized for the Muslim woman."
This is from the European Council of Fatwa and Research (http://www.islamopediaonline.org/fatwa/european-council-fatwa-and-research-question-women-traveling-alone-not-un-marriageable-kin).
This website also has a comprehensive view on the matter: http://www.islamandquran.org/fatwas/the-traveling-of-the-woman-without-mahram.html (read to the end)

All this being said, there are numerous hadith that did primarily state it as being unpermissible for women to travel alone, due to the lack of security and due to the context that the Prophet lived in: in the Arabian desert fifteen hundred years ago. However, many prominent and very learned scholars have stated that should the woman take her safety precautions, it is permissible to travel alone.

Conclusion:
I believe that we can put these five previous points together:
If we add having pure intentions in all that we do (point 1), the purpose of worship in all that we do (point 2), the equality of men and women in the eyes of God (point 3), with the good news that the Prophet gave about women being able to travel alone in the future (point 4), as well as the contextualized ijtihad of current learned scholars (point 5), then I think we can conclude that women are indeed permitted to travel alone.

Important note:
I am not a scholar. Please do your own research on this topic and follow what you believe to be correct using your reason and your heart. I have simply provided the reasons that I have come to my own conclusion, which also happens to be an opinion shared by many. If there are parents who believe that their girls should not travel alone, then there might be other issues, such as a lack of trust or not identifying the girl as being responsible or independent enough. However, I believe that a woman of age, should be able to make her own reasonable decisions, given the advice of loved ones and of trusted mentors/scholars. Once again, this is a blog post, not a fatwa.

Finally:
Honestly, I will defend this right to freedom and independence until the day I die because it is so central to who I am and what I believe in. So there it is. I have said it. And Allah knows best :)