If you have an ActiveSync or Exchange server (like work or gmail), you can setup the account as an e-mail --> Microsoft Exchange. For example, if you want to sync your g-mail calendar and contacts only.
E-Mail app --> menu --> settings --> plus sign in upper corner --> gmail address and password (DO NOT PRESS NEXT) --> press Manual setup --> Microsoft Exchange ActiveSync --> and use these settings:
Domain\username: google\your-email@gmail.com
Password: *******
Exchange server: m.google.com
Then click next --> ok --> uncheck sync e-mail and notiffy --> check calendar and contacts
This works for any activesync and exchange server, but you need to have the domain and server settings from your e-mail provider.