Quite a number of free fax services have come and gone over recent years. I don't know of any one current service that lets you both send and receive faxes for free without a lot of restrictions, but that doesn't mean you can't have your fax and send it too! All you need to do is use two free services, one to send your faxes and another to receive faxes.
FaxZero allows you to send a limited number of short faxes for free. At this writing you can send two faxes per day of up to three pages each. It may not be high volume, but it can come in handy when you need to get few pages faxed out. The free faxes have an advertisement on the cover page. There is no registration required and you can send faxes for free to anywhere in the US and Canada.
To receive faxes for free you can get a free US fax number from FaxDigits. Your faxes are delivered as a PDF file to your email inbox. They don't place a limit on the number of free faxes you can receive. You can't choose the location of your free fax number. My free fax number is an Iowa number, which is not surprising, since that it where the company is located.
Either of these services alone is pretty nice, but the combined services are almost like having a free fax machine.