One thing that I'd like that we've had with our landline providers for a years is the option for multiple voice mail boxes, so that the caller selects who they want want to leave a message for. If each could be assigned an email address to notify that would be great too.
This was my first wish and still my most pressing need.
"For Mom, Press 1"
"For Dad, Press 2"
"For Sis, Press 3"
"For Bro, Press 4"
Then each mailbox can be individually configured to forward email or SMS text to the appropriate person.
Internet login also allows sorting my messages unique to each box, so I don't have to look through all the rest of my family's calls.