yes you can.
In linux there is a program called wine http://www.winehq.org/
You can also use "crossover Office" or "Cedega" for games.
Not all windows applications are compatible.
The other option is to install a virtual machine through a program called VMWARE.
This will install a whole linux system in windows or a windows system in linux. There is very little compatibility issues doing it this way accept Graphics drivers will not work so 3D games are out of the question.
There are other products as well such as WinforLin and I think Mandrake linux has an option to install linux in windows.
Do a google search for these products.
NOTE: The wine product is free however the others cost money unless you get hold of illegal keys.