You can install applications in the user application folder to make them only available to that user. However, the default location is the system application folder so unless you purposely put it in your user application folder, you won't have any there.
It's not abnormal to have an applications folder in your user (home) folder. I have one there. Why some don't, I have no clue, maybe it's something that's a carry over from older versions of OS X, or maybe clean installs of Snow Leopard without copying any data over from a previous install doesn't have it? But either way, having one there is nothing to worry about, especially if it's empty.
Apple - Support - Discussions - Applications Folder In Home Folder? ...