You can simply backup the folder in documents\electronicarts\thesims3 and move that to your new computer.
You will need to reinstall the game itself but you can then replace the new folder that is being created with your old one and it will be as if you started the game on your old one (all savegames and custom content will still be there.
You probably delete all the cache files and any logs though
Here's some info on the files in that folder: http://sims3.crinrict.com/en/2011/01/faq-user-files.html
