If you're having problems with your Exchange Account reaching its maximum size limit, then the course of action needed to be taken is:

For Outlook:
Open up Outlook.
Click on File in the upper left corner.
Click on Data File Management.
Click on the add button.
Click on Office Outlook Personal Folders File (.pst).
Click Ok.
Choose a name for the archive file and put it into the File Name area.
Click Ok.
Put the name that you choose to give to your archive folder in the Name under General.
Click Ok.
Click Close.
Now that you have created a Archive Folder do the following:
If you want put folders that you have under your mailbox, just drag that folder from your mailbox and put it over the new archive folder until it is highlighted and then let go. That should place the folder under the new archive folder.
If you want to create new folders under the new archive:
Right click on the new archive.
Click on New Folder.
Name the folder.
Add your emails to the new folder by drag and drop or by right clicking on the email you want to move.
Click on Move to Folder.
Select where you want to place the email.

For Entourage:

There are two main things you can do in Entourage to speed it up and prevent the full mailbox message.

First, make sure that your deleted items are truly being deleted. Along the left side of the Entourage window, under the "Exchange" section, click on the "Deleted Items"
Left side menu

If you see that there are email messages that should have been deleted a long time ago (say several weeks) then it appears that Entourage is not emptying the trash each time you quit like it should.

To fix this, go to the "Tools" menu and find the "Schedules" option near the bottom of the menu. The Schedules window should now pop up.
Schedules window

It is possible that a rule already exists that says something about deleting items, but as we've seen that rule is not doing its job, so you can delete that rule by clicking on it once and hitting the "Delete" button on the top of the window.

Now click the "New" button and the "Edit Schedule" window will come up. Fill in/configure the fields like this:
Name: "Empty Deleted Items Folder"
When: "On Quit"
Action: "Delete Mail"
from: click on the drop down menu, go to "Choose Folder..." and find the "Deleted Items" folder under the Exchange section.
Choose Folder

Older than: The default is 7 days, but you can set it to whatever you'd like.
Dial-up options: leave alone
Enabled: checked
Now click the "OK" button and close the Schedules window by clicking the red button in the top left.

The next thing to do is archive your old mail onto your computer. This stores your old messages in a folder on your computer instead of on the server, freeing up server space for new mail.

Along the left side of the Entourage window, right click click (or control click) the "Folders on My Computer" item and a menu should pop up.
Menu

Click on the "New Subfolder" item and a new folder will pop up in that section. Name it "Archived Mail" or whatever you'd like to, and then hit return.

Now click on the "Tools" menu and find the "Rules" item. The window that pops up has several tabs across the top such as Mail (POP) and Mail (IMAP). Click on the one that says Mail (Exchange), then click "New," and the Edit Rule window will pop up. Fill out the fields like this:

-Rule name: Archive Mail
-If: Click on the drop down menu that says "All messages" and select "Date Received"
-Now a new menu will appear, set to "Is." Click on it and change it to "Is greater than," then set the number of days. This number is really up to you.
-Once you archive your mail you can still get to it just like you would any other mail, but only from the computer you're archiving it on, so it's not accessible from the Outlook Web Access or someone else's computer, so it would be wise to use something like 60 days.

Under the "Then" segment, there should be two lines of drop down menus, like this.
Two lines

Click just to the right of one of the lines so that a faint blue box appears around that line and then click the "Remove Action" button which should have become bright.

Now in the first drop down menu, select "Move Message," and in the second drop down box, select "Choose Folder..." and navigate to the folder you previously made.
Finished box

Now you can click "OK" and close the Rules window. From now on, when messages get over 60 days old, they will automatically get moved into your Archived Mail folder where you can easily find them, but they won't take up valuable server space. To apply this to existing mail messages, highlight a folder (such as Inbox, Sent, etc) by clicking on it once and under the "Message" menu, go down to the "Apply Rule" item, and in its little pop up window, select "Archive Mail." Entourage will now go through your Inbox looking for any messages older than 60 days (or whatever you set it to) and archive them, preventing you from getting the error message.