Calling/skype, various messaging apps, podcasts, music, weather, bus app, email, calendar, chess clock. There are some things that wouldn't work (games, video). These are fairly low priority for me. Some things that might sorta work, especially if they were re-made for e-ink (eg maps/navigation apps). These I want on my phone.
An e-ink phone might not be a bad idea if it could carry other advantages too. A $200 smartphone with 3 day batteries that runs 80% of apps might be appealing to a lot of people.