You can, although make sure to keep track of your e-mail usage, otherwise you could end up running out of storage space.
If you chose to leave your messages on the mail server, and you don’t clean out your mailbox every once and a while, you will eventually run out of space, and messages to your mailbox will start being bounced from our mail system.
The time it takes for this to happen, solely depends on the volume size of messages you normally receive.