These are the minimum requirements posted by EA. Basically with a system matching what's below you'll be able to run the game and it'll be mostly playable, but not on high settings and you can expect lag.
THE SIMS 3 MINIMUM HARDWARE REQUIREMENTS
FOR WINDOWS XP
* Windows XP (Service Pack 2)
* 2.0 GHz P4 processor or equivalent
* 1 GB RAM
* At least 6.5 GB of hard drive space with at least 1 GB additional space for custom content
* 128 MB Video Card with support for Pixel Shader 2.0
FOR WINDOWS VISTA
* Windows Vista (Service Pack 1)
* 2.4 GHz P4 processor or equivalent
* 1.5 GB RAM
* At least 6.5 GB of hard drive space with at least 1 GB additional space for custom content
* 128 MB Video Card with support for Pixel Shader 2.0
For computers using built-in graphics chipsets, the game requires at least:
* Intel Integrated Chipset, GMA X3000 or above.
* 2.6 GHz Pentium D CPU, or 1.8 GHz Core 2 Duo, or equivalent
* 0.5 GB additional RAM
