Software

There are a ton of different application you can use, it comes down to a few questions. Did you want the remote machine to be running a daemon that will allow you to connect whenever you want or do you prefer to use something ad hoc.

If you do a quick google you'll be presented with a list of options including, goto assist, logmein, teamviewer, VNC, windows RDP, SSH, to name a few.

Try Remote Utilities. It has an affordable Home license and is very powerful.

I have used teamviewer a lot. You can try that. It is free. You have to install it on both machines. It will create an ID & password for both machines. you can define your own fixed password also. now u just have to put the id of the other machine & click on 'remote control' button. Then it will ask for the password & after that you will be able to see & work on the desktop of that machine from your screen. Always click on 'personal/non-commercial use' while installing or whenever it asks.
thanks

http://www.screenconnect.com/
https://logmein.com/
http://www.teamviewer.com/
http://www.mikogo.com/
http://www.techinline.com/
http://www.bomgar.com

here are a few options for you. there are many more.

try this program, it runs straight from the website basically - http://www.ammyy.com/en/

If you would like to have BIOS level access to the remote computer, you should use KVM over IP. I am using this one for our remote office in Sweden http://minicom.com/kvm_px.htm

If you are administering computers and they are Windows based RDP works great. Where RDP becomes cumbersome is when you want to do training or have the user show you what they are doing or it's a non MS OS. In those instances I use VNC. (you can use RDP for "over the shoulder" control, but it isn't as slick and easy as VNC)

If you are coming from an iOS or Android based device I highly recommend the Wyse PocketCloud Pro app which supports VNC and RDP along with SSL.