How can I detect what exact version of Exchange server I connect to with Outlook?

Right click the outlook icon in the task bar while holding the CRTL key then select connection status. Move the scroll bar all the way over to the right to see the version number, and compare the number with the below Versions

Microsoft Exchange Server 2000:         6.0.4417 or higher
Microsoft Exchange Server 2000 SP1:     6.0.4712 or higher
Microsoft Exchange Server 2000 SP2:     6.0.5762 or higher
Microsoft Exchange Server 2000 SP3:     6.0.6249 or higher
Microsoft Exchange Server 2003:         6.5.6944 or higher
Microsoft Exchange Server 2003 SP1:     6.5.7226 or higher
Microsoft Exchange Server 2003 SP2:     6.5.7638 or higher
Microsoft Exchange Server 2007:         8.0.685.24 or higher

They don't specify a version for 2010 so I'll include it: The RTM version of Exchange 2010 is 14.00.0639.021 and the SP1 version of Exchange 2010 is 14.01.0218.015.

Source

Currently the only way to find the version was to access the web interface (OWA). Inside the Account section you will a numeric version written in the left sidebar.