Exchange allows you to sync a max of 10 devices agains a mailbox. Each time you sync a new device, a sync partnershipe is created.  You can view thes sync pertnerships in OWA.  Most users will never see this error code; however, IT professionals who test and develop EAS devices will sometimes run into this issue. 

Exchange will respond with a 177 error if you go over the limit.  Since this error code is pretty high ( ie over a hundred) so you would find information on that code in the Common Status Codes section of of the MS-ASCMD protocal document:

2.2.4 Common Status Codes
http://msdn.microsoft.com/en-us/library/ee218647(EXCHG.80).aspx

177

MaximumDevicesReached

The user's account has too
  many device partnerships. Delete partnerships on the server before proceeding.

You can see the device partnerships if you log into OWA and click on Options -> See All Options,click on Phone and then click on the Mobile Phones icon.  If you
double-click on one you will probably see text such as the following:

You currently have 10 Exchange ActiveSync partnerships out of 10 maximum partnerships allowed per user. After you reach the maximum, no new partnerships
can be created until you remove some from your account.

You can delete a partnership by selecting a partnership and clicking on the fancy X icon above the list. You can also use the Exchange PowerShell command Remove-ActiveSyncDevice:

               
Remove-ActiveSyncDevice
http://technet.microsoft.com/en-us/library/bb125032.aspx

Another thing to think about is to change what the maximum number of partnerships is.  This is something which your Exchange Administrator would need to do using the Powershell Set-ThrottlingPolicy command.

Set-ThrottlingPolicy
http://technet.microsoft.com/en-us/library/dd298094.aspx

The syntax is something like: Set-ThrottlingPolicy –EASMaxDevices 50 –Identity
DefaultThrottlingPolicy_xxxxxxxxxxxxxx

Please note that my expertise is not with the Exchange PowerShell cmdlets, so I'm not going to go into the details on this command.

For EAS development,  you  should consider having all your code be able to handle 177 and any other of the  common status codes.  For your development and testing needs I would imagine that you would likely want to increase this limit.