I spent a fair amount of time using one computer to look at/control another across the internet. Over the past 5 years I have evaluated a number of products. The following are some of my favourites.
This is the best option across a wan, giving good performance. However it is a pain in the proverbial to set up for use across the internet, as the ports are frequently blocked by firewalls.
LogMeIn is the one I use must frequently, for controlling my personal computers. A free account will let you control a reasonable number of computers (5 I think). The paying version has additional features such as file access, sound and printing. I have used the free version for about 5 years.
Install is straight forward, go to the web site, log in, install software and go. The software takes care of firewall and NAT issues in nearly every case. In 5 years, I only found one location where I couldn't get connectivity.
There is software available for nearly everything, I have even used my windows mobile cellphone to control my pc.
It's account based, so it is good for computers I own. It is not so good for other computers where I don't have physical access beforehand as I obviously don't want to pass my account details around. Once installed, the client pc can be unattended.
GotoMyPc is an alternative, but they don't have a free version.
I use crossloop (no relation) for remote user support. They download and install crossloop and I do the same. They click on the share button, send me the access code, and then I connect using the same access code. Performance is not as good as LogMeIn, but it is usually adequate.
It does require a user on the client machine to run the software, hit the share button and provide the access code. It's free to use.
CoPilot is an alternative which is probably better for Grandma and technically challenged users. It's free on weekends, and $5 a day during the week.