What about having a party with everyone as siblings probably avenging their parents. Usually you play with everyone as strangers and meeting up just to get gold or whatever but if you're already blood related that can make for different role-playing.
Hunter,
I do like these threads. I was actually in a game that was something like this. Rather than all being related they all knew each other and came from the same region and were extracting revenge for a great evil perpetrated on them. It was great fun while it lasted. The main difference being that we role played a group that knew each other, and thus was more prone to work together… although the Dungeon Master dictated a few rivalries, as one might expect from groups that know each other.
Being all related by blood or from the same village you can find some interesting role play. One may feel the other is getting more powerful for their britches and want to make sure they stay humble and may do it in interesting ways. Yes many personal rivals can come out of a game like this. It does change a lot of the dynamics.