On the trains you can pay cash (or at least you could very recently when I stupidly left my EzLink card on my desk at home). The ticketing machines (GTM) have an option to pay a cash fare. However, there are at least 3 disadvantages to this.

1.) The cash fare is more expensive than the EzLink fare for the same distance

2.) You cannot use it to transfer to busses (changing trains is okay though)

3.) You have to put down a $1 deposit for the ticket (which is a smart card like the EzLink). If the fare is, say $1.50, you have to pay $2.50. Once you get to the destination, you have to put the card back into a ticketing machine to get $1 back.