I've been using
Interfax for some years (email to fax) and have never had a problem. Not "free" though.
Normally I email a PDF and then one can be sure of what the end fax will look like.
As for sending a fax directly from a computer, one can do it with e.g. Winfax (a once nice program which Symantec trashed (like most things they touch) and then discontinued) or using the built-in fax in Windoze (which is pretty flakey IME). Winfax is OK once you have it set up, with a normal old-style modem, but is flakey with GSM/GPRS/3G modems so for mobile fax one tends to be back to email2fax services.
The other thing is that when faxing over GSM one needs a really good a constant signal, much better than is needed for internet connectivity, and this also favours email2fax.