There are a variety apps that you can use to remotely control a computer. Using VPN, you can also access computers on another network.
Some apps only work with Windows computers, some only work with Macs, and some work with both. Some require third party software to be installed on the computer you need to control.
iTeleport is a very effective VNC client. It is very responsive, even on 3G, and it has never crashed on me.
I have now switched to the VNC client "Screens". The advantage over iTeleport is that with iTeleport, you control the mouse with our finger. Your finger does not have to be on top of the cursor, but you have to move the cursor to wherever you want to click using your finger. It works, but it is a bit like rubbing your stomach and patting your head because your finger does not correspond to where the cursor is. Screens on the other hand essentially transforms the remote computer into a touch-screen-based computer. Your finger becomes the cursor.
Here is an example to better describe the difference. Lets say the cursor on your remote computer is currently at the top of the screen and you want to launch an application that is in the dock at the bottom of your screen:
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