(updated August 21, 2015)
What is the largest mission agency?
It depends on your definition.
If you're looking for manpower...
and you consider Cru (Campus Crusade for Christ) a mission organization, then they are the largest with about 25,000 staff worldwide(1), although a large amount of them serve in the US and about 60% of their funds are spent in the US.(2)
Another possibility could be Gospel for Asia with around 16,500 missionaries.(3)
Another possibility could be Christian Aid Missions. It gets a little complicated, but basically they support over 500 indigenous missions ministries, which deploy tens of thousands of missionaries (4) (over 800 ministries and 80,000 missionaries the last time it was posted on their website (5)). However, the amount of funding they give would only be enough to fully support about 3,000 missionaries.
If you count short-term mission workers, YWAM (Youth With A Mission) sends around 25,000 short-term workers every year(6) and also has a staff of over 18,000, the vast majority of whom are in the US. (7)
If you are looking for the organization that sends the most missionaries to another country as foreign missionaries, Wycliffe Bible Translators is likely the largest. They send about 5,000. In other words, if you don't count national missionaries, Wycliffe is the largest. (8)
If you are willing to count volunteer evangelists, Gideons has over 300,000 members worldwide, but the vast majority are not serving in a capacity that would qualify them as a 'missionary'. (9)
If you are looking for the organization with the largest budget...
It would be Cru with $694 million in world revenue (10) or if they aren't considered a mission organization, it would be International Mission Board with a budget of $301 million.(11) YWAM might have a large budget as well, but YWAM is decentralized, so I guess we have no way of knowing without a lot of extra research.
Using Operation World's definition of a missionary (on page 949-950) and their lists, Cru is the largest with 9,913 missionaries, while Gospel for Asia is second with 9,550. (12)
If you are wondering what mission organization is the largest by way of having planted the most churches...
well that's a blog post for another day.
Last thing I want to say is that bigger doesn't necessarily mean better. A ministry might be a large ministry, but it might not be effective. Also, be careful of comparisons. We need to see ourselves as being on the same team. Too often in the past, denominations or organizations have only concerned themselves with "Where are we, and where aren't we?", rather than "Where are disciples, and where aren't disciples?" It shouldn't be about a particular brand of Christianity having the most pins on a map in the foyer. We're all a part of the body of Christ.
1. Laurie Goodstein, "Campus Crusade for Christ Is Renamed," The New York Times, July 20, 2011, http://www.nytimes.com/2011/07/21/us/21brfs-CAMPUSCRUSAD_BRF.html?_r=0.
2. Cru 2014 Annual Report, (2015), 12, http://www.cru.org/content/dam/cru/about/2014-cru-annual-report.pdf
3. 2007 Gospel for Asia Annual Report: A Year of Joy, (2008), 21. (The 2007 annual report was the last time Gospel for Asia published the number of missionaries they have. The current number is unknown to the public and may even be less, based on the use of funds in Indian foreign contribution filings.)
4. Christian Aid Mission. http://www.christianaid.org/home/1/home.aspx (accessed August 21, 2015).
5. Internet Archive: Wayback Machine, "Christian Aid Mission: Discover Indigenous Missions, (July 30, 2013)," https://web.archive.org/web/20130730121146/http://www.christianaid.org/home/1/home.aspx (accessed August 21, 2015).
6. YWAM: Youth With a Mission Cancun. http://ywamcancun.org/index-en.php?sec=who-are (accessed August 21, 2015).
7. YWAM: Youth With A Mission Worldwide, "About Us," http://www.ywam.org/about-us/ (accessed August 21, 2015).
8. Jason Mandryk, Operation World: The Definitive Prayer Guide to Every Nation Completely Revised-7th Edition (Colorado Springs, CO: Biblica Publishing, 2010), 948.
9. The Gideons International, "About Us: Worldwide Impact," http://www.gideons.org/AboutUs/WorldwideImpact.aspx (accessed August 21, 2015)
10. See note 2 above.
11. IMB Connecting, "Fast Facts," http://www.imb.org/about-us/1307.aspx#.VdexAflVhBd (accessed August 21, 2015)
12. Jason Mandryk, Operation World: The Definitive Prayer Guide to Every Nation Completely Revised-7th Edition (Colorado Springs, CO: Biblica Publishing, 2010), 939-950.