If I was to be given a billion dollars with no option of refusing or returning it, I would consult a lawyer to open a blind trust to accept the money as an anonymous trustee. If at all possible, I wouldn't publicize my name with this money. All charity donations and projects would be done anonymously.
I like many ideas which have been stated. Similar to Jaben, I would change my life to focus more on empowering others to realize the benefits of understanding the power of positive thinking and the abundance mindset.
I would consult financial advisors to set up investment planning to ensure that like Nobel Prizes, the principal could grow and interest could finance things like:
a) an educational foundation: to undertake projects that raise awareness of literacy, writing, arithmetic, spiritual and cultural values worldwide. Scholarships would be available for learning and grants would be available to build/ repair schools and provide teaching materials as well as to fund innovative teaching programs like International Space University and Highschools which take place on ships which sail around the world and offer practical education in different countries. I like Ablix's idea which would invite parents to be involved in schooling for their children. I would also donate money to charities such as summer camps for sick children and the Children's Wish Foundation where terminally-ill children could realize dreams.
b) raising health awareness: to finance vaccinations, train doctors, midwives and health professionals, support doctors-without-borders in developing countries, and to support hospital projects like Dr. Catherine Hamelin's hospital in Ethiopia which was built to perform life-saving fistula operations.
c) scientific and environmental research projects: to develop and research energy-saving alternatives and encourage changes in lifestyle, reduce global warming and other natural disasters. I would offer incentives to develop teleportation & other means of travel which don't depend on fossil fuels.
mtrimpe has interesting ideas, but since 2/3 of the planet doesn't yet have access to telephones, then a global vision for the Internet may not work as effectively as if this was combined other approaches.
Like Ethereal, I would also devote more effort to my own spiritual development. This would include trips to remote, spiritual places like Bhutan.