I finally settled on Remote RDP Lite 3.0.6. The lite version has some capabilities disabled and allows only one saved connection (with the pay version you can save many RDP connections in the list and just tap on one to connect). But even the lite version is fairly robust. All my computers that allow RDP using port 3389 worked fine with this app.
Any IT professional with an Android device will like this app, and find it very useful.
The other app that is very nice for RDP/VNC is PocketCloud from Wyse. It also will only allow one profile unless you purchase the full version. It has audible feedback and everything is done through the touch screen without a mouse pointer (Remote RDP has a mouse pointer which you move around). I personally found it harder to move around in PocketCloud. A definite pro for the Wyse product is the better GUI and the ability to choose between installing a local client on machines you wish to remote into or not. If you do choose to install the local client the app has the ability to autodiscover.
It is my personal preference, but I find the Remote RDP product easier to use.