As fo3nix says, ISDN is very slow compared with broadband. However it is available in some areas where DSL is not (for example, where I am).
ISDN provides two digital channels each of 64K, which means you can either use channel bonding to get a 128k connection, or (like most people), use one channel for a 64K connection, leaving the other channel free for analog phone, fax and modem calls. One 64k channel can carry two analog signals, so (for example) I can be talking to a customer on the phone whilst looking at their computer via an internet connection, and still someone else in the office can be sending a fax, talking on the phone, or even using dialup connection to the internet.
It works out much more expensive than DSL.
Oh one other thing, you can opt to have MSN (multiple subscriber numbering) which means that you can have 3 different phone numbers, so you could use one unpublished number for your net connection, and publish the other two as phone and fax.
Another advantage of ISDN is if you need a point to point connection with another computer. As long as they also have ISDN, you can call them directly without needing to go via the internet. I use this method to connect to my bank in London (much safer than Internet banking).