Update - this no longer works in iOS 10 as Apple has finally implemented playing movies from iCloud. If you try this trick now you will end up renting the movie regardless of whether you have the physical space available or not
I came across this great trick for saving space on an iOS (updated to iOS 9.3) device the other day - and having used it on my 16Gb iPad Air 2 I was able to move from having 650Mb free to 3Gb free without deleting any content !
The trick involves navigating to the iTunes Store using the iTunes Store app, having first noted down the amount of available space you have (under settings >> general), and then going to Movies and attempting to rent a movie that is sized over the amount of free space you have. You can determine the size of a movie download by scrolling down and reviewing it's details - HD movies are normally a few GB in size at least. When you select "Rent This Movie" your device will complain that there isn't enough space and provide you with a pop up message that advises you this and suggests you go to Settings - if you follow the route to your device settings you will notice that, as if by magic, your available space has now increased slightly !
Simply repeating this process will incrementally increase the available space on your device - I did this about 6 times to get from the 650Mb to 3Gb free. You don't actually end up spending any cash on renting the movie - just make sure the size of the movie is always more than the free space you already have !
A great tip courtesy of iMore.