If your team are all Apple users (in part), the Apple calendar is pretty good for sharing.<p>We use different email apps, but our email's provided by Media Temple as our hosting's with them. I rate Airmail pretty highly if you've got a Mac.
Google Apps works like a champ.
We do use Trello's calender features for some stuff as well because we can link to tasks we've got set up within Trello itself.