You can turn aging off if you want to, but then no Sims will die.
A few additions to the comments here. Scientists from GTW can use the cloning machine to make unlimited copies of Potion of youth and/or the scientist life serum (forget the actual name. too lazy to look up atm). Ghosts are a form of semi-immortality. They don't age anymore, and they can do anything a Sim can do accept have children. Depending on your goals, just moving a dead Sim's ghost into the household can be good enough. Scientist can also use an upgraded cloning machine to clone a Sim. Not quite immortality, and a failed attempt can produce an "evil twin" with different traits. But a successfully copied Sim has all traits, including reward and aspiration traits of the original. They don't have the skills, job promotions, relationships etc of the original and they start with a randomized name. The original Sim also lives on.
Also, the cow plant has to kill another Sim in order to extend life, so it's not the option for everyone.
Pregnancy will extend life by a few days in some cases, because Sims won't age up autonomously while they are preggers (it might still be possible to go from YA to adult with a cake. Never tested it so I don't know).
With the life extending potions, wait until the Sim's birthday to use them so that you maximize their effect. Their life bar will turn "glowey" when they are a few hours away from aging up autonomously. I usually wait until this happens to drink the potion of youth.