I have been using Back to my mac and it works great. I was able to play a game over the internet just like I was sitting in front of my computer.
Of course there is a slight delay, but it is very usable. I used a wi-fi connection to a 50MB home cable connection. It was fascinating to see the system automatically adjust the screen and colors. It was a free flash game from Kongregate. If you had a regular full frame game like a Shooter or something, it probably wouldn’t be playable.
However what the average person does with a remote connection is grab a file or look at something on their own computer. I have used LogMeIn as well in the past for remote connection and while it was cool, it also costs money to work well. Currently there is some question whether a free remote access tool TeamViewer is safe. There is much discussion about people who have it and have said they have lost money or files while it is in use. To me, I never was impressed with TeamViewer. I always thought VNC was faster and better. TeamViewer also has the unfortunate reputation of being used by scammers, so for that alone it is worth avoiding and blocking on a network.
Of course there are other tools that are free to remotely connect to a mac or PC. A very safe tool from apple is called Apple Remote Desktop. This is usually used by a mac administrator in a company network to manage macs. I have used that in the past and it really is neat what it can do. For PC’s you can use the built-in Microsoft RDP client. That requires the end computers to be configured usually through group policy.
So you can always access your files, even if you don’t use cloud storage.