We considered this but in discussion we decided against it. Too many of our kids keep copies in their room to call friends. Many of us keep an extra copy in the car to reach people when we are on the go. Online would just tie us to the computer too much. But we can print our directory very cheaply at the district's print facility - under $100 for a 1000 copies, we have 800 students. We sell about $1000 in ads, so directory actually makes money.
We did this for the first time this year. Just a couple people complained. I honestly think not many used the directory anyway. We tell them one reason is to save money, and another to save trees; they can just look the name up and not have to print it, or they can print only their child's class, or whatever they need. We do make sure that parents who fill out a form asking us not to publish certain things (email, cell phone #, address, whatever) are deleted. You don't need a password to access; we thought that it would be just as easy for John Doe to pass someone's address/phone # on from the online directory as it would be from the paper one. We did consider that there are a few, just a few, families without computers; however, since there are assignments that have to be done using the internet and/or PowerPoint, whatever, they must have access to a computer somewhere..... Or could ask a friend to print the directory for them. I could even print them one....
One question to consider, Do all of your families have a computer and the internet? At my son's school not everyone has the internet, some cannot afford and others do not their children on the internet.