Please note: the following is my understanding and simplified view of a complex landscape of options and protocols
It is intended to provide insight for the inexperienced, rather than a complete and accurate technical description

If you are reading this as a customer of another ISP then just assume that every mention of Bigpond is a reference to your provider. While things that are true of bigpond might not be true of your provider this should still get you most of the way there

Bigpond and others provide email addresses for free with their services, but in reality this is nothing more than a trap to prevent you from switching to another service – in my opinion there is no reason for a Bigpond customer to use one of these addresses

Apple iCloud, Gmail, Yahoo, Hotmail etc. are portable when you switch to a different Internet Service Provider and remain capable of being used with standard settings anywhere in the world (as do properly setup self hosted emails like myname@myowndomain.whatever)

A bigpond address often fails to send when you are not connected to the Telstra provided infrastructure forcing users to access expensive solutions like global data roaming or clunky solutions like webmail

In addition a Bigpond address is not designed (at time of writing) to properly sync between multiple devices

Why? Bigpond use a protocol known as POP which offers advantages for the provider including reduced ‘chattiness’ between devices and the email server, but none for the user – especially when the user has more than one device*

*status of messages (flagged, read, unread, deleted, forwarded, replied) is not echoed between devices

Other protocols exist – IMAP, Exchange, Google Sync, iCloud

Exchange is a Proprietary (Paid) Microsoft protocol which supports multiple devices for mail, calendar, contacts and notes
It is typically used by businesses with their own domain

Google Sync is similar to Exchange and is apparently based on it
Google Sync, with the right settings makes it easy to sync mail, calender, contacts and notes between iPad, iPhone and presumably other mobile devices
while it works well on mobile, due to licencing restrictions, it doesn’t work fully on the desktop and is quite frustrating and time consuming to configure on a PC or Mac (Purchasing Outlook may be a solution to this)
One major advantage of Google Sync is the ability to set it up with your own domain
Update: Unless you were already using Google Sync or a paying Google Customer, Google Sync is effectively dead – http://support.google.com/a/bin/answer.py?hl=en&answer=2716936

iCloud is a proprietary (free) protocol for those who own one or more Apple computing devices
iCloud makes it easy to sync mail, calender, contacts, notes, bookmarks, documents, location, device backups, reminders between all of those devices and a few items can sync with a PC running the iCloud Control Panel

IMAP is a non proprietary email protocol which works on any device, but must be supported by the provider of your email;

Bigpond – does NOT support IMAP
(email addresses ending in bigpond.com or similar)

Gmail – Supports IMAP, but I have seen the uninitiated become confused by the way Gmail handles IMAP
(email addresses ending in gmail.com)

iCloud – Supports IMAP, but setting up as iCloud is easier (iCloud email can be easily used on PCs with Outlook, Macs, iPod, iPhone and iPad. Setting up on a different device requires careful configuration)
(email addresses ending mac.com, me.com, icloud.com)

email addresses ending in internode.com, adam.on.net, yourdomain.com, yahoo.com, hotmail.com, iPrimus.com
Internode – Supports IMAP
Adam – Supports IMAP
Your own hosted email may or may not support IMAP, although most do
Other providers like Yahoo, Hotmail, Dodo, iPrimus etc. may or may not support IMAP to one degree or another

POP – Some of these emails support POP, but I generally recommend avoiding it. If you have a bigpond address which you have shared with many people and you now use multiple devices it is normally*** best to switch to an iCloud or Gmail address and have your incoming Bigpond emails redirected there

***Not all bigpond addresses are equal. In all cases we can forward emails received at a bigpond address to another address, but it is not always possible to prevent the bigpond inbox from continuing to fill up requiring us to keep checking in

Update:I have experienced varying interfaces with Bigpond webmail and settings.
In all cases those settings allow mail to be forwarded to another address, but most of the time there is no option to stop the Bigpond inbox from continuing to fill up. Since writing this blogpost I have helped people set this up 3 or 4 times and it is starting to appear as though address ending bigpond.com are of the inferior variety (inbox continues to fill) while those ending in bigpond.net.au appear to be capable of forwarding emails WITHOUT, at the same time, continuing to fill up themselves

We can use pieces of each protocol – for example

A bigpond user might use POP for his email, but use iCloud for his Calendar and Contacts

A Gmail, internode or Adam user might use IMAP for email and Notes with iCloud for Calendar and Contacts

While these solutions work they require more configuration than a single solution like Exchange or iCloud (Google Sync is similar but much less easy unless we are only interested in using mobile devices)

iCloud seems to be the best overall solution, but your needs will vary depending on your email address, willingness or ability to change address, current devices, future devices

Now go and have a lie down…

Update:Adam it appears do not allow email addresses provided by them to be forwarded at all – if you are an Adam customer I recommend avoiding their free email accounts like the plague

Update March 6, 2013:Chariot – www,chariot.net.au – also omit options for forwarding, but a call to their helpdesk reveals that they can set it up manually for you