I used to work for a company that provided support for Google Apps for Business (including Outlook through the Google Apps Sync tool), and a lot of the most common requests we received were as follows:

- Ability to forward multiple emails at once (as far as I know, native support for this doesn't exist in Gmail, though an extension is available).

- IMAP and POP3 are (surprisingly) still being utilised a lot more than you may think; I once asked a customer why they were still using POP and they explained that it helped them feel more in 'control' of their data as IMAP and other forms of syncing are merely representations of the emails themselves (including the WebUI), whereas POP3 gave them the ability to download a physical copy to store away - they didn't fully trust the whole 'cloud' concept and believed that segments (if not all) of their email could potentially disappear sporadically, which wasn't entirely implausible.

- Backups. These were often a concern for customers, and it was quite a while until Google Vault was opened to end-users (at an extra charge). I feel it's having that peace of mind that matters, and without that users often contacted us requesting batches of messages to be restored, which can cause complications based on the TOC regarding data protection.

- Consistent visibility of all email accounts (particularly amongst Apple Mail users); i.e. a list of each email account they own (regardless of provider) on the left-hand panel showing the primary mailboxes (Inbox, Sent, Drafts, etc.) This extended to iOS through the default Mail app (not sure if this is still a limitation preventing this functionality with recent versions of iOS).

- Saving drafts or unread emails addressed to self as a way of keeping notes and reminders. I do know that Gmail (unless they still do) allow you to synchronise 'Notes' in iOS via native Mail app which then creates a 'Notes' folder in Gmail, where each 'note' is stored as an email with minimal message-body information. I found a lot of customers preferred this kind of ideal rather than relying on another external solution for their notes.

- Push notifications; something that IMAP doesn't support out the box, where HTTPS protocols such as Exchange ActiveSync would be required for this.

- Synchronising flags and categories for email (and contacts); something that was never supported in Google Apps Sync.

- Automatic setup of email based on incoming MX record values (like how Thunderbird does it!)

- Synchronisation of calendars, contacts, tasks, notes, etc. in addition to email. This is often a common request, and where it was supported by the Google Apps Sync tool, Apple Mail users would have to use separate tools (iCal, Address Book, Tasks?) to synchronise these. Outlook 2011 was available, but only synced email (unless cross-synchronised with iCal, quite messy).

Beyond feature requests, we frequently received reports from customers with PST corruptions and where this may be partly due to incompatibilities with the sync tool, PST does not seem like a stable format in which to store important email data. I've also seen situations where mail clients (commonly Apple Mail via IMAP) have deleted every message from the cloud mailbox store, resulting in requests to restore these messages or the arduous process of dragging and dropping those locally cached messages back into their Gmail mailbox -- those were long, drawn out phone calls; good times :)

I reckon your biggest challenge will be not just be in providing native cross-platform support, but rather cross-mail provider support. One of (if not the most) of the common issues we received from users were IMAP bandwidth limits being hit consistently, where Gmail imposes a limit on how much mail can be synchronised an hour/day/month. This was frequently reported for Apple Mail, to which I found related to the amount of active IMAP connections it keeps open to the server, and the frequency of any resulting requests. I imagine this was implemented for the sake of speed, but didn't play well with Gmail's limits.

We had a small number of users that used Thunderbird and I found it to be quite user-friendly compared to other mail clients I've tested; automatic account setup and optional modules (for migrating mail, syncing other data, etc.) being highlights here. I find the modular concept great here, and you can see it being used in Gmail in the form of 'Labs'. Some users like to have a minimal setup, so being able to choose your own features is a plus on many levels.

That's most of what I can think of for the meantime and I hope it helps. Do let me know if you'd like to discuss any of the above in more detail and I'll provide any further feedback where I can.

Best of luck!