Test Cases for 16-bit Ripple Carry Adder
Whenever feasible, a full test is a safe choice. With 2\$^{32}\$ input permutations, a fast chip, and some patience this might just be feasible. (At 1 test per us it would take less than 2 hours.)

When just 'testing an adder' and no time for a full test, I would go for a random test.

But in your case you know that i is a ripple adder, and you could include the carrys in your output. That means that you can test each section independently, by choosing suitable inputs. That means only about 16 * ( 2 ^ 3 ) test vectors (each combination of A B and carry, and that for each section). That is a small test test, but because you can check the carries it still has full coverage.