Weak health: these sims get sick all the time, the illness have more effect and sims stay sick longer (like 1 of 2 days instead of 3 hours) medicine won't help.
Competitive: these sims always want to win and will even cheat to achieve that. If they lose a game they will get angry or even cry.
Stupid (or maybe unintelligent sounds nicer): these sims are bad at school, no matter how hard they study they'll never score more than a 6 (a C).
Adults won't get promoted higher then level 7 in carreers, no matter how hard they work.
Besides more traits and bigger effects, I would love favourites like favourite food, color, hobby's, sexual orientation, etc.