These are the tiebreak systems most suitable for men's events.  There has still never been an improvement on the tiebreak for women's events, naked jello wrestling.

Usually there are several tiebreakers that can be used.  The best is of course some sort of direct playoff, but time may not permit this. 

In Swiss events, the first tiebreaker is often an adjusted one.  For instance, a common method is to calculate the sum of the total scores of each player's opponents (unplayed games like byes or forfeits count as 0), drop the highest and lowest, and the resulting number is the tiebreak score.

An easy secondary tiebreak is just to put the dropped scores back on, which will usually produce a winner.  But if it doesn't there are other common tiebreak systems.

The Sonneborn-Berger system (which was designed for round robin events) allots each player the total score of the players he defeated, half the score of those he drew, and nothing for the games he lost.

The Cumulative system is thought by some to be the ideal Swiss tiebreaker:  the players running scores on the wall charts are added up.  A player who goes 1-2-3-4-4 in a five round event has played a stronger opposition than one who scores 0-1-2-3-4, although they are tied at the end, because Swiss tournaments pair players with similar scores, so the first example has been playing the tournament leaders since the first round, where the second has come in the back door against weaker players throughout.

These are the tiebreak systems most suitable for men's events.  There has still never been an improvement on the tiebreak for women's events, naked jello wrestling.