According to Wikipedia, FIFA uses the following list of tiebreakers when deciding who qualifies to participate in the World Cup (i.e. who gets to compete in the World Cup at all, not who qualifies from the group stages of the World Cup to the knockout rounds):
- Points (3 points for a win, 1 point for a draw, 0 points for a loss)
- Overall goal difference
- Overall goals scored
- Points in matches between tied teams
- Goal difference in matches between tied teams
- Goals scored in matches between tied teams
- Away goals scored in matches between tied teams (if the tie is only between two teams in home-and-away league format)
- Fair play points (based on the number of yellow and red cards given)
- Drawing of lots by the FIFA Organising Committee
What's the record for how far down the list they've needed to go? Have they ever needed to go beyond "overall goals scored"?