The above pic is from the United States Air Force Thunderbirds history page. Note that it uses the wrong homophone.
A hangar is a big garage for airplanes. A hanger is something that is used to hang things (e.g., clothes, shelves, ornaments).
This is how I personally learned to remember the difference: h-a-n-gar (age). I think it’s ironic that the Thunderbird pilots and their support crew are so amazing in traveling all over the country doing airshows with no crashes, perfect formations and superb attention to detail, yet their web master fails to pay the same attention to their public-facing site.
(Don’t roll your eyes! It’s important to us grammar-obsessive, plane-spotting nerds.)
Hangar
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Hanger
Next hanged and hung.