The most I've ever had was 7, with a single mother to boot! I had two Sims at first. At first it was just a set of twins, then the wife gave birth to triplets. A bit later I decided to let them have one more child, since there was only room for one more Sim, so no possibility to twins, right?
Wrong. Two days before the wife gave birth, her husband get singed while repairing the stereo. This was early on in my Simming career, so I didn't realize that trying to repair stuff while singed was... unwise, to say the very least. Long story short, the wife was now left with a dead husband, five young children, and still pregnant. Of course, since the husband had died, there was now room for twins, and guess what happened?
So, she had to raise seven children all by herself. It was a harrowing few weeks, to be sure.