The NFL has an interesting approach for overtime in the regular season,* where a draw is still possible but 'modified sudden death' applies. Basically, if you receive the ball on a kick off and score a touchdown, you win. If you only kick a field goal, then the team that kicked off receives the ball and has a chance to equalize with a field goal or win with a touchdown. If they equalize, then it goes to true sudden death. If after the overtime period of 15 minutes there is no winner, then a tie is declared. Ties are rare, but in a truly tight contest are very possible.
It's good because it encourages teams to play attacking football on their first possession, since a field goal just gives the ball back to the opposition and actually creates the conditions for potentially losing.
Not sure I'm keen on the idea for rugby, but it's interesting to discuss variations beyond the Golden Point (which I agree sucks).
*In the playoffs, they keep playing overtime periods until one side wins.