Troubleshooting does not have to be expensive, nor does daily administration of your mail servers and messaging environment. There are, in fact, a wealth of resources available for Exchange administrators to monitor health, administer users, migrate mailboxes to the cloud and even take care of old data that is stored insecurely and uncatalogued. But it's often difficult to know where to look for these software assists.
These tools are all aimed at Exchange 2010 Service Pack 1 and up, including Exchange Online and Office 365, although I have noted where previous versions of Exchange are supported by each of these tools.
Out of the 10 tools shown here, nine are free; all should be part of any Exchange administrator's toolbox.