Scholarship and contest awards can greatly reduce the financial burden of travel. Some will give you a money amount, while others will award based on expenses (e.g. a free flight, free accommodation), some will be a mixture, and some will be all-inclusive. Be sure to read the fine print of all of the contests, as they may require some kind of project, research, or display of the program in return.
Here are some scholarships or contests you can apply for right now:
WorldNomads Travel Photography Scholarship Competition 2013 Deadline: July 5, 2013
Win a trip to Queensland, Australia for 5 days (bloggers only) Deadline: June 23, 2013
Win a trip for two to Brazil (21+ only) Deadline: June 30, 2013
Win two tickets to Norway on IcelandAir Deadline: July 2, 2013
And here are some annual or ongoing scholarships and contests:
Boren Scholarship: This scholarship sends US undergraduates to critical areas of the world, where they learn uncommonly taught languages. Funded by the NSEP. Deadline: ongoing, see site for details
Critical Language Scholarship Program: Funded by the US Dept. of State, students can travel to critical areas of the world and spend a summer, fully funded, learning a language that the US government sees an interest in. Mostly for students hoping to pursue a career in foreign affairs. Deadline: Fall 2013 for Summer 2014
Win a flight anywhere on Turkish Airlines: Two winners per month, random drawing.
Win a $500 Expedia travel voucher: All you have to do is participate in #ExpediaChat on Wednesday afternoons on Twitter.