Should I help pay my parents mortgage or buy my own place?

Because of the historically low mortgage rates today it would be a mistake to use your cash to pay down their mortgage. There are numerous places to invest your money that would give you a bigger return than you would be saving in interest and even if you couldn't do better there is a lot of value in maintaining your liquidity. If they need help I think your best option is to ist them making part of their mortgage payment.