In a lot of games where you can take various 'handicaps' for characters most players will take advantage of these to no end. One common I have seen a lot of is games consider having a family or dependent to take care of is a handicap or something bad. That or they write up a character background where they have a family and then forget they even exist once play starts. This is a bit assbackwards in my mind but it seems to be the way a lot of games and players go. Well if they want to take them as a disadvantage or completely ignore them then by all means make them the biggest problem in their ass that you can.
Never ever kill the family. I know for some folks running games out there this is going to be really hard. It flies in the face of tradition of killing off the PC's beloved by the players. Problem is it is usually only effective for one game session and then it's blown off. Don't do that, keep them alive, that way they can continue to be a problem to be dealt with.
Now with that first bit out of the way lets look at a bunch of basic ways to aggravate.
Old debts come calling. Somebody owes somebody else a lot of money and they want that money now. Debt collectors come in many forms and sizes, from collection agencies calling up people related to (or responsible for) the debtor to more aggressive tactics like showing up at their front doors. Times this by ten if the person they owe money to is a criminal organization or massive gambling debts. Easiest way out of this is simply paying them what is owed... if they can. Otherwise it may build up to actual physical conflicts to be endured.
If their dependent is a child well then those cost money... trust me I have a couple. So be sure to hit them up for cash spent between game sessions. Food, clothing, school costs, toys, games, etc. This creates a constant drain to the pocket book and we Gamemasters know how important it is to separate a character from their money. Failure to provide a safe and healthy home is considered negligence in the eyes of the law in most civilized places.
If the character has a wife well then those cost money also... trust me I have plenty of broke friends to testify to this. Be sure to have them spending it for them as often as possible. New clothes, a car and all it's costs, etc. It doesn't have to be the rude stereotype of a 'money spending woman' either, but if they aren't bringing in income they have to be given something to survive on also.
Kids are a never ending source of headaches, some being worse than others. Make your PC's kids part of the 'worse' section. Calls from the police if they get caught shoplifting an angry shop owner if it's a fantasy world. Running away from home in the middle of the night. Having to go pick them up in east jesus when they are tired, cold and hungry. Be sure a lot of this suddenly pops up in the middle of the game so they have to take care of it right then.
Tag along. You can't always leave them at home and sometimes they just utterly refuse to stay there. Be it a baby sitter canceling at the last minute or a wife who thinks her riding along won't be any problem. Just put them there beside them for the entire game... talking... asking questions... doing the wrong things at the wrong time. You get the idea.
The borrowers. You get out on the adventure just to discover some of your rations are gone and that extra lamp oil is missing. Well you know, somebody back at home needed that, they just didn't bother to tell you. Same goes for finding your hard drive space filled up with downloaded movies or the extra fuel can being empty. Or when they do return something they took without telling you it's because there is now something wrong with them. The IR goggles are on the fritz (because IR goggles are damn cool to any kid out there), that computer has a virus from the downloaded movies or scope on the rifle is knocked out of line.
Poor choice in friends. Your daughter is hooked up with a sleazebag who has a tendency to steal anything left out... and he's at your house when the adventure is on. Your wife has a friend who is constant trouble with the law... and your wife is always trying to help bail her out of trouble. Your son has been hanging out with some vandals... and they've all been picked up by the police.
Don't forget the old standby use of a family member in a game. Kidnap them so you have to rush to the rescue.
There is just so much you could use to stick it to your players with their family. Make that disadvantage one hell of a disadvantage. If you do it right they won't look at it as a fast way to get some extra character points next time. Just remember to keep them alive so they can be a pain over and over again.