ActiveSync isn't really a type of mail account. Exchange uses ActiveSync as does Hotmail, Live, and "Google as Exchange". "As Exchange" means ActiveSync.
Exchange should not be grouped with Google. Exchange requires an Exchange server. Gmail and Google Apps accounts are not hosted on Exchange servers.
Where are options for IMAP and POP accounts? Both are very widely used.
Poll is pointless until it is corrected. You need to sort out whether you're asking about the type of email account or how they're connected (e.g. Hotmail can be ActiveSync or POP, Gmail can be ActiveSync, IMAP or POP).
Exchange is an MS product. You can't have a non-MS Exchange server.
There's another option that is frequently overlooked: hosted Exchange. I use Apptix.