After some googling, it appears that Windows Mobile 6 does indeed include a Remote Desktop client. However, some manufaturers choose not to install this software onto their phones by default. Worse, there's (seemingly) no way for the end user to install it. For example, I have a T-Mobile Wing with WM6, and I couldn't find the remote desktop software on the phone. It appears that T-Mobile opted not to install it. Not cool.
So, after yet more googling, I found a .CAB file of an unofficial Remote Desktop client for WM6. I've tested it out and it seems to work great...I remote-controlled both a Vista & XP machine on my home network using my Wing.
To install, download this Windows Mobile 6 Remote Desktop client, unzip it somewhere, and then copy the WM6RDP.cab file to your phone (using ActiveSync in XP, or WM Device Center in Vista). Next, on your phone, simply click the 'WM6RDP.cab' file to install it. It will then appear in the 'Start -> Programs' menu as 'WM6 Remote Desktop.'
More information on this download is available here.
Update 7/22/08: A couple updates on this. First, if you're having trouble getting the keyboard to work with this RDP client, make sure that you installed the WM6RDP.cab file to your device's main memory and not to the storage card! More info on that here.
Second, some people have asked me if there is a newer version available and—to my knowledge—there is no update available.