AFreeRDP and AndroidVNC, Windows has remote desktop built in so the other paid apps seem a bit of a kludge to do something Windows already provisions for. I run an OpenVPN server on my router that bridges my phone onto my LAN from public WiFi or 4G. Most of the time my computers are running Linux and for that I use terminal emulator with ssh or AFreeRDP+xrdp or AndroidVNC...Linux (Ubuntu GNOME 13.10 in my case) has a lot of nice remote access solutions available and they work well. All free and open source too.
Sent from my SM-N9005 using xda app-developers app
Samsung Galaxy Note 3 SM-900T 32GB
Samsung Galaxy Note SGH-i717 16GB
HP TouchPad 32GB
Archos 43 Internet Tablet - 16GB + 32GB mSD
Dell Axim X50v - 128MB + 16GB CF