Finding the Windows version of a remote machine in the same network

As Josh King noted you can use srvinfo which is a Windows 2003 Resource Kit tool.

On Windows 7 you can use systeminfo

systeminfo /s remote_computer_name

To get just the hostname and OS from systeminfo pipe in findstr, this eliminates the other noise

systeminfo /s [machine name]|findstr /i "host OS "

nmap can perform remote OS detection.

It's not 100% accurate, but you'll have to see for yourself.

Here is an example result. I specifically picked a result that wasn't 100% accurate, but this machine is a Windows Server 2008.

Warning: OSScan results may be unreliable because we could not find at least 1 open and 1 closed port
Device type: general purpose
Running (JUST GUESSING): Microsoft Windows Vista|2008|7 (98%)
Aggressive OS guesses: Microsoft Windows Vista SP0 or SP1, Server 2008 SP1, or Windows 7 (98%), Microsoft Windows Server 2008 (98%), Microsoft Windows 7 Professional (97%), Microsoft Windows Vista Business SP1 (93%), Microsoft Windows Vista Home Premium SP1 (93%), Microsoft Windows Server 2008 SP2 (91%), Microsoft Windows Vista Home Premium SP1, Windows 7, or Server 2008 (91%), Microsoft Windows 7 (90%)
No exact OS matches for host (test conditions non-ideal).