Sims with the Family Aspiration long to be part of a big, happy family. They need "Quality Time" with family members, and lots of meaningful interactions with all the branches of their family tree. Keep their Aspiration Meters overflowing with familial bliss, and they'll live long and "fruitful" lives.
Family is an Aspiration in The Sims 2. Family Sims aspire to get married and have children, as well as having "Quality Time" with their family members. Starting as a teenager, Sims already want to fall in love and go steady with their lover. The next important phase for Family Sims is in Young Adult or Adult: to get engaged and married. After that, they will usually want to have many babies. Teens will want to go steady with another Sim. Elders will want grandchilden.
As the Sims' family is growing, they will want their grownup children to get engaged and married, and eventually want to see their grandchildren. Family Sims will love to spend their quality time in Winter[TS2:S], since it's the time to spend with family. Also, they want to constantly keep pets[TS2:P].
Family Sims have high-impact fears about relatives dying, losing friends and being rejected for interactions by their children or grandchildren. Sims who reach aspiration desperation will pull out a sack of flour with a face painted on it and will begin to rock and cuddle it, as if it was a baby.
It is not recommended to pair a Romance Sim with a Family Sim, because their wants will clash, since Romance Sims fear commitments.
If one wants to pair a Family Sim with someone that doesn't also have the Family aspiration, the easiest are a Fortune Sim or a Knowledge Sim, since their wants won't clash very easily. Fortune Sims make particularly good partners for Family Sims, as their desire to earn raises and promotions will leave their spouses free to be homemakers and stay-at-home parents. Knowledge Sims make good co-parents for Family Sims, as they roll wants to teach toddler skills and study skills more frequently than most other aspirations.
You should create a family Sim married or at least with one (or more) children, because most of the family Sims' lifetime want is "marry off six children" (or "have six grandchildren") and that is something very hard to achieve, so you have to make a lot of children, and fast. Also recommended is to adopt children when they are children and not babies or toddlers.
Sometimes Family Sims get "Have a Child" as both a want and a fear. It's unknown why this happens, though it may be because they have just had a child and don't want the stress of another even though the aspiration makes them want one. Still, having another child is worth a net 3,000 ASP.
When returning from work, Family Sims will occasionally launch into an "I'm home!" animation, even if no one else is home. This can be stopped by canceling the "At Work" icon in the Sim's action queue, but if it is not canceled, it will run for about 30 game minutes. There is a mod by Cyjon that will suppress this.
Townies and NPCs with the zodiac sign of Aquarius or Cancer generally have this aspiration.
Having the Family aspiration may not prevent Sims from wanting to flirt with another Sim, even if the former is already in a relationship.