Haven't tested it yet, but I am a sucker for at least trying non-game apps that are free. http://www.amazon.com/mobile-apps/b/ref=sa_menu_adr_app4?ie=UTF8&node=2350149011
Amazon.com: Appstore for Android
Find, shop for and buy at Amazon.com
Let me know how you like it, after you've tried it.
I've been using PocketCloud to do this, but it's an annual subscription, so if I can pay once and use forever, I'd switch to this.
Alternatively you could get it for free now and try it later. :)
I use logmein on the iPhone and it works great. I have the free version. The android version is 29.00.
Just played around with it a bit and it works exactly as expected. It requires an app to install on the system (i.e., doesn't work natively with Windows RDP), but it works and is very easy to set up. They also have a feature where you can log into their little streamer program (that you install on the PC/Mac) that allows you to log in with your Google account and, theoretically, if that is the same Google account you use on your phone/tablet you can access your computer anywhere. I've only tested this at home, so I haven't tested the true nature of "anywhere" yet.
For free? It's solid. I think I'll use it periodically for any remote desktop I may need.