Adoption/family causes and performing arts access for kids are two of the main things near and dear to my heart. I always encourage people to find a personal connection or at least an organization that is very transparent about where their funds go and the work they are doing. These are some of my considerations:
Overseas, I am skeptical of big aid organizations. I visited both Japan and Haiti post-disasters. The people I met there had seen little, if any of the aid money sent reach the people in need. I also tend to support people who are working towards long-term solutions and stability, not just band-aiding the problems. (Of course there are many situations, especially when there's been a natural disaster, that need some short-term help as well.)
I am also wary of sponsorship programs. Sometimes they are keeping children in orphanages rather than empowering their parents to support them. (Especially in countries like Haiti, where most of the "orphans" have living parents and many of the "orphanages" are run by corrupt people looking to make money off rich foreigners. Orphans and adoption ethics is a big issue being talked about right now, especially pertaining to Haiti. I suggest reading some of Jen Hatmaker's stuff as well as the Livesays. Their blog about life as a family of ex-pats working with a maternity ministry in Haiti is generally amazing and inspiring.)
I would rather support local economies and send money to an organization that buys products made in impoverished countries than ship toy/clothes/food to people in need from the U.S.
Organizations I Support:
A Family For Every Child
A local organization that is dedicated to finding loving, permanent families for every waiting foster child. One of the programs they run is the Heart Gallery, where photographers take portraits of foster children and the photos are displayed around town in an effort to raise awareness about adopting from foster care. (I'm not sure if it's them or another organization here that also sets up a tree at the mall, where you can pick a child's name and get them a Christmas gift. It's a really cool way for kids to participate in giving. My little brother always has a great time picking a toy out for a kid who's in the situation he was once in.)
My grandparents run this ministry to the local homeless community. They do everything from large events with free food and music to just serving hot coffee and making friends with people.
Hosanna Performing Arts Foundation
Sharing the gospel through performing arts, mainly dance through outreach performances by youth and adult companies, as well as Adventures in Narnia, a yearly holiday ballet portraying C.S. Lewis's The Lion, The Witch and The Wardrobe. I've been involved with HPAF with Narnia and now Hosanna Dance Company.
Working to keep families together in Port-Au-Prince, Haiti. They provide jobs to parents, mainly making artisan goods and jewelry from recycled materials. I admire their commitment to understanding and helping the Haitian people support themselves and rebuild their economy with dignity. The founders are long-time friends of my family and I had the privilege of spending a few weeks teaching knitting at their artisan workplace in 2012.
Seeds of Hope International Partnerships
Located in Zambia, SOHIP's focus is on reversing poverty and creating healthy homes. They employ locals to manufacture concrete bio-sand filters. They provide these super simple and efficient water filtration systems to families and do community health, nutrition and sanitation training. They also do agriculture and business development and share the gospel in the communities their working in. They're run by the uncle of one of my best friends, and she was able to visit with her parents last summer and help pioneer a sewing program.
I also love the concept of Advent Conspiracy. Their idea is to put the focus of Christmas on Christ not Consumerism. They encourage people to focus on spending less (money on stuff), giving more (time, relationships), loving all, and worshiping fully. The past few years the church I was involved in raised thousands of dollars and divided them between local ministries and Advent Conspiracy's water charity.
Do your research. Ask questions. Pray and listen. Support things that move you personally. Share locally and abroad. Give generously.