Fire

They can be burned to death through a fire caused by the Fireworks Launcher, the Barbecue, the Stove and the Fireplace. Apparently, Sims can also spontaneously combust. I have never had this happen to one of my Sims and assume it is quite rare. Prevention: Ensure your Sims have at least a few cooking skill points before allowing them to cook a meal.

Don't place objects directly next to a fireplace, they will catch fire. Always play with the Fireworks Launcher outside as it will almost always cause a fire if launched indoors. Place smoke alarms in every room so the fire department will be called automatically.

Cure: Have your other Sims attempt to "extinguish" the burning Sim. If you're fast enough, they may be spared.

Drowning

Sims won't generally drown on their own. Usually you would need to entice them in, then remove the ladders.

Prevention: Don't let your Sims swim when they have very little energy.

Sickness

If your home has a Guinea pig and you don't keep it's cage clean, your Sim has a chance of getting sick when the guinea pig bites him/her. A sick Sim will often cough and sneeze. Prevention: Keep the guinea pig cage clean. Cure: Lots of coffee and rest, keep the comfort and energy need meters up. Have the sick Sim "view" the guinea pig painting (LL).

 Brew a white potion on the Chemistry Set (LL) and have the sick Sim drink it.

Starvation

If your Sims hunger meter drops to zero for several days, they will suffer a most slow and unpleasant death.

Prevention: Make sure your Sims always have money on hand so they can order pizza or get food from the fridge or barbecue.

Cure: Buy a fridge and get your Sim a job, paint a picture, sell some furniture, anything to get your Sim a few simoleons(§) for at least a snack.

Electrocution

Any adult Sim may instantly die from electrocution when attempting to fix an appliance or change a light bulb.

Prevention: Make sure your "handyman" Sim has at least 5 mechanical skill points before asking them to fix something. Make sure your Sim is not standing in a puddle of water when fixing an appliance. Call a handyman instead, they will fix any household problems for you.