More details on which receipts you need to keep. Quick takeaway: Receipts > $82.50 inc GST
Practically, we use the ATO rules on when you claim a GST credit as a guide on when you should have a receipt, as this sets a reasonable guide for order of magnitude and can be subject to audit.
According to this:
You must have a tax invoice to claim a GST credit for purchases that cost more than $82.50 (including GST).
For (minor) expenses below this, other methods of substantiation can be used (eg a line on a bank statement, xero feed etc).
If you are an employee wanting to claim back an expense, you should snap a copy of the receipts to include in your expense report for your employer to claim back. Note that many employers have a straight forward "No receipt, no reimbursement" policy - ie you effectively need a receipt for reimbursement even if its a $4 coffee.