The PC and Family

Families are not usually important to members of the typical adventuring party, though this has changed somewhat since the introduction of the "Bond" feature. They were, however, key to the survival and identity formation of people in non-modern societies (and continue to be today, especially if we agree with the contention that we have never been modern).

If adventurers don't concentrate exclusively on slaughtering monsters, and wouldn't mind having some kin, but their players and Game Masters both have other things to think about, rolling on a table is always an option. It may spark the player's interest,  especially if an older brother means a chance to borrow some money, or even to recruit a new meat shield to bring into the dungeon.

Parents:

As an option, to provide an incentive to figuring out whether a character has parents or not, allow the starting character to double his or her wealth if both parents are living, and multiply it by 1.5 if only one parent is living. Assuming the character is in good standing with the fam, that is.

d8 roll

1. The character is an orphan who grew up with strangers (never knew parents)
2. Both parents are deceased (but known by the PC)
3. Character is a black sheep
4. Only father is living
5. Only mother is living
6. Both parents are living
7. Character grew up with other relatives (grandparents, aunts, etc.)
8. Other (character had multiple families of origin, grew up in non-standard/polygamous family, etc.)

Siblings:

This is an admittedly idiosyncratic table suited to a fairy-tale environment (which is what I run). It can easily be changed to reflect a more realistic situation. 

It is possible that some results will conflict with those of the Parents table, so ignore or rationalize inconsistent results.

d12 roll

1. PC is the youngest of three children of the same sex
2. PC is the youngest of seven children of the same sex
3. PC has a younger sibling of the opposite sex that he/she is responsible for
4. PC has an older sibling of the opposite sex who is responsible for her/him
5. PC is the only child of a widowed mother who obsessively dotes on him/her
6. PC's mother died, father remarried. Stepmother has a child from a previous marriage, and she and the step-sibling hate the PC
7. PC was a foundling adopted by an elderly couple (only child)
8. PC has three siblings of the opposite sex, and is responsible for marrying them off
9. PC has an identical twin (who may or may not be the PC's polar opposite)
10. PC and a fraternal twin of the opposite sex are children of a widowed parent who has remarried
11. PC has a "named" sibling (may be of a different people or race) who has sworn to aid him/her in an hour of need
12. Player choice: anything other than any of the above

Family of Procreation:

If anything, this comes up even less frequently than the question of parents/siblings, but can be a great stimulant to play (if a character is adventuring to find a match, or, conversely, to get away from an unsuccessful marriage).

d8 roll

1. PC is single and innocent
2. PC is single and experienced (may be unmarriageable as a result)
3. PC is promised to someone
4. PC is married but (still) childless
5. PC is married, with 1d4 children
6. PC is widowed, with no children
7. PC is widowed, with 1d4 children
8. Player's choice (vow of celibacy, polygamy, cohabiting, same-sex relationship, etc.)