How can you measure how good a random generator is?

Recently, I tried to make some random generators myself. But I wondered how you could measure how good they actually were. First I thought, you could for example compute pi with them (with monte carlo) and then look how close it is the the real one. But then I realised that with that method a generator that just rises x from 0 to 1 and then rises y a little bit and just continues doing this until y = 1 (so it just equally distributes points all over the plane) would outperform any random generator. So how can you measure it then?