I'm helping a user with Outlook 2010. They have a large mailbox that they want to sync over IMAP, but we want to not sync the whole thing in order to keep Outlook performing well. A lot of email clients (especially those on smartphones) allow you to say "Only sync the past .... days" where you can choose a week, a month, two months, etc. Does Outlook allow for this, or is there any way that I can fake the functionality?
There is no way I know of to do that. You can only choose to download headers, or full e-mails (HIGHLY recommended in my opinion). I would also recommend that you teach users to not store too many items in one folder, since that seems to affect performance. In general, for IMAP, it is just slow with larger mailboxes.
Ultimately, if you want excellent performance with large mailboxes, and quick synchronization times, I can't recommend hosted Exchange enough. I have multiple clients using it, including a lawyer's office where they must keep everything, and it performs extremely well. Some of the users have as much as 12GB of mail, and it synchronizes header changes in seconds from a server 3000 miles away....only after that does it pull the bodies and attachments.
If you do choose to go this route, come back and I can offer some concrete advice on how to make the move, because I encountered numerous pitfalls the first time I went from IMAP to hosted Exchange, including who I would go with and why.
Since you're using Gmail, you might consider the Google Apps Sync for Microsoft Outlook. It lets you set a hard mailbox size limit for Outlook. For example, if you set the limit to 1 GB, the Sync tool will begin removing older messages when you hit the limit (the emails are still available in Gmail though!)
Download here: www.google.com/apps/intl/en/business/outlook_sync.html
You can specify a number of latest messages to sync in Gmail > Settings > Forwarding and POP/IMAP > Limit IMAP folders to contain no more than this many messages > set desired number.
I dealt a bit differently with the same issue, where a user wants to use Outlook with Google Apps for Business. You can just go to Gmail settings and under "Forwarding and POP/IMAP" tab, change option "Limit IMAP folders to contain no more than this many messages" to 1000 (which is the lowest number). This will make Outlook download only 1000 latest emails. It works without a problem.
Here is avery good explanation I found on microsoft office help:
Click File > Account Settings > Account Settings
Select an Exchange account, and then click Change
Under Offline Settings, move the slider to the desired amount of time, such as All, 12 months, 6 months, 3 months, or 1 month.
For example, if you move the slider to 3 months, only mail from the past three months will be synchronized to your Offline Outlook Data (.ost) file from the Exchange server. Items older than 3 months reside only in your mailbox on the server. You can change this setting at any time.
Change how much mail to keep offline (answers your "Only sync the past .... days" question)
Download headers only
Download items and attachments smaller than a specified size
Create a Microsoft Exchange account synchronization filter
This feature requires you to use a Microsoft Exchange Server 2000, Exchange Server 2003, or Exchange Server 2007 account. Most home and personal accounts do not use Microsoft Exchange. For more information about Microsoft Exchange accounts and how to determine which version of Exchange your account connects to, see the links in the See Also section.
Synchronization filters allow you to choose which items are downloaded or kept in your Offline Folder file (.ost). The .ost file is used when you work offline or use Cached Exchange Mode.
The next time the folder is synchronized, any new or modified items in the .ost file are uploaded, all items matching the filter are downloaded, and items that do not match the filter are removed from the local copy.
Reduce mail download sizes (gives you much more options)