I want a service that allows me to use my own domain name. It's going to take a while before I can actually stop checking my several gmail accounts. I don't want to have to make the switch between email services again. Although I need the security of knowing I can do so. My gmail isn't portable, anything at my own domain name is.
Make email more like messaging. Message threads would be topic and user based like email (messaging is just user based) and fully searchable. Allow for longer message bodies than typical messaging and attachments. Make the threads tag-able to help with searching and create a easy interface to find attachment files.
My issues with email are: #1 spam. Make your system invite / friending only #2 searching typically sucks. Ever get those "I sent you that file already" or "we talked about that 2 months ago". Make sorting and grouping by topic easier to navigate.
If you'll be developing a GMail alternative, it would be nice if you can personalize the look and the way how you'll be receiving and sending emails quite different from the norm. It would be better if there's a feature where you can set sending and receiving emails on different platforms. Shall we say, you can only received emails on specific contact via phone app and once received will no longer have a duplicate on the desktop browser version.