Since the installation process can be quite hard with Vanilla WINE, a PlayOnLinux script has been created by NSLW, that makes the installation very easy. I thought I just create a short guide on how to install The Sims 3 with PlayOnLinux.
First of all, you need the latest PlayOnLinux. Go to PlayOnLinux downloads and download the latest version. Install PlayOnLinux and start it from the start menu or with the command 'playonlinux'. Select 'Install' -> 'Games' -> 'The Sims 3' and follow the installation script.
The script will install some dependencies and the game and you will then be prompted to enter your graphics card Video RAM size.
Since the copy protection doesn't work with WINE, you'll have to download a NO-CD patch and replace the original files with the cracked ones. You will find the fake Windows folder in /home/USERNAME/.PlayOnLinux/wineprefix/TheSims3/drive_c/. I will of course not provide you with any information on where to get these files.
Here is a gameplay video: