I like this simple square:

11 66 98 89

99 88 16 61

86 91 69 18

68 19 81 96

In the square, every row, column and diagonal adds to 264. If you study it a bit more closely you should be able to see the simple principle behind it. However, what makes it particularly magical is that if you turn the square upside down, it becomes what appears to be a different magic square, but with the same magic total.

(In fact all of the numbers on the original square are simply mapped onto new positions in the inverted square, though it takes a while to figure out what the rule is for which goes where.)