Generally speaking, no, not without an external internet fax service.
Your DSL / ADSL / ISDN / cable broadband internet connection will normally be a data connection to which you are connected with a data modem (not data/fax modem). This means that you can only send and receive data from your internet service provider (ISP) on this line, and cannot send and receive faxes*.
If you have an old data/fax modem, you cannot connected to the broadband connections, but you can try connecting it to another phone line or to the phone connection of your ADSL splitter. Note however, that some ADSL splitters have been known to have problems with handling the high-pitched tones of fax transmissions.
Internet fax service providers are ideally suited for working with DSL / ADSL / ISDN / cable broadband internet connections. An extensive list of internet fax services can be found on this site at http://www.faxbeep.com/internet-fax-service/. At the time of this writing**, efax, ClickFax and Myfax are the most-discussed services
*Technically speaking, some ISDN modems are data/fax modems which behave like data/fax modems on regular, analog lines, but this is the exception and not the rule.
**Updated May 2005