I'm running with 4GB RAM and an ATI X850XT card - game and graphics (set to high) are fine except that I get a CTD after I've used CAS to modify clothing or appearance.  I discovered that if I immediately save after exiting CAS, no crash. 

That said, I allowed the 12-year old to play TS3 under a different account on my computer.  CTD.  I saw two warning popups claiming that a script running under Internet Explorer had stopped running (this appears only in the secondary account).  WTF???   EAxis up to no good in the background no doubt, because I disconnect my DSL modem before starting up the game and never use IE.

The crashes continued each time she tried to play until I changed the firewall setting by not closing it down completely, but setting it to block all Internet activity.  That's worked for her.   

My firewall is set so that no EAxis program has permission to access the Internet.  Since it appears to continue trying, I'll have to experiment with the ZA kill command.

Another weird thing that happened at the Sekemoto's I never noticed elsewhere (and didn't screen-capture as it happened so quick) was this:
Sam, while still a Toddler, seemed to be tring to stand up while another Sim crossed the room next to him and, briefly, Sam's neck and torso and head stretched until the top of his elongated bald head was about at standing-Toddler height. Before I could even fumble for the pause button, he quickly glooped back to his normal Toddler dimensions.

I have a feeling the stretchy-Toddler thing has something to do with my computer struggling to keep up with a bunch a High Detail animations on a busy lot (this happened while guests were arriving for Sam's Birthday Party) but I can't figure out the music-in-Yumi's-head thing.

CTD? What does that stand for? Crash to desktop?

What about your other specs, it's certainly not the card. As that card shouldn't have any issues with sims...