My rewrite of the tie-breaker rules

• Standings should be determined by win-percentage, by which I mean points-percentage, but W% just looks and sounds better.
• The first tie-breaker should be total points. For example, a team that is 4-4-0 is tied in W% with a team that is 3-3-0, but prevails based on points earned (8 and 6, respectively). No matter how you determine the standings, there are going to be weird side-effects, all of which have to do with discrepancies in games-played. The trick is to choose the least offensive effects. The way we have it currently (in the real NHL), a team that is is 5-7 (10 points) is ranked higher than a team that's 4-4 (8 points), despite the fact that no-one, looking at the records, thinks 5-7 is a preferable (i.e. better) record. My proposal, emphasizing W% before points, would lead to odd effects like 6-3-0 teams being tied with 4-2-0 teams and 2-1-0 teams, while a 7-7-0 team would be beneath all of them. However, the trade-off is worth it, because when we get to the meat of the schedule, after the first few weeks, W% is a much more accurate way to rank the teams. You won't have anomalies like teams being artificially high in the standings because they've played 6 more games than everyone else (like Anaheim, in the middle of this year). 
• The second tie-breaker should be regulation wins. Not regulation plus OT wins. Just regulation wins. My reasoning: let's say Team A has a record of 20-10-0 with 10 of those 20 wins in OT, and Team B is 20-10-0 with all of its wins in regulation. Both teams have the same W% (.667) and the same total points (40), but Team B has allowed its opponents to earn 20 points which Team A has allowed opponents to earn 30 points. In the big picture, we all know that a regulation win is more valuable than an OT win (we're seeing it every day in the playoff race). A team that allows its opponents to earn fewer points is better than a team that has the same number of wins but also allows its opponents lots of Bettman points. 

If Two Teams are Tied

• The third tie-breaker should be head-to-head points, points earned by those two teams in head-to-head games. 
• [UPDATE] The "odd games" rule for the head-to-head tie-breaker (which ignores the first home game played by a team which has played one more home game than another team -- in mid-season ties) should be eliminated. Obviously, the idea behind that rule is to recognize that it's fundamentally unfair for one team to have more home games than another. However, I think it's pretty obvious that it's even less fair to ignore the outcome of an entire game. Also, the odd home games issue can only come up mid-season (or in the cup finals, see below), and mid-season it's largely irrelevant except when dealing with the waiver wire, which allows teams to make claims in reverse order of standings. If GMs are especially worried about the waiver order issue, they could institute the odd home game elimination rule for the purposes of the waiver order only. 
• The fourth tie-breaker should be head-to-head goal-differential. Tally the number of goals-scored by Team A against Team B and Team B against Team A. We're still trying to determine the better team. Total goals not only is the logical next step, but it would make every goal count, even the last several goals of a blow-out. 
• If the tied teams are in the same division, the fifth tie-breaker should be record within the division, and then -- if records within the division are equal -- record within the conference. This would give greater weight to divisional rivalries, which intensifies those rivalries. Otherwise, why have divisions?
• If the tied teams are not in the same division, the fifth tie-breaker should be record within the conference. 
• The sixth tie-breaker should be points-earned against conference teams with better records than the tied-teams in question. For example, if Team A and Team B are tied for 6th in the West, then the record of Team A against the teams in 1st-5th place is compared to the record of Team B against those same teams. My reasoning: a team that beats better teams is better than a team that doesn't. (Yes, it's also true that a team that loses to worse teams is worse than a team that doesn't, but shut up consider that we informally make this comparison all the time; we say, "Team A and Team B have the same record, but Team A has a losing record against playoff-bound teams..." or "Yes, they're tied, but Team B is in a weak division..." )
• The seventh tie-breaker is goal-differential (not head to head, but for all games-played).
• [UPDATE] I actually think it would be better if the seventh tie-breaker were goal-differential per game in games against teams with better records than the tied teams. 
• The eighth tie-breaker is goal-differential within the conference.
• The ninth tie-breaker, if the tied teams are in the same division, is goal-differential within the division. 
• The tenth tie-breaker, is a coin-flip. Exception: if the tie involves two teams tied for the 8th and 9th spots at the conclusion of the regular season, the two teams will play a single-elimination tie-breaker game to determine the winner. (but see: "three or more teams are tied" below.) 

If Three or More Teams are Tied

• The third tie-breaker is head-to-head(-to-head-to-head etc.) points earned among the tied teams. 
• [UPDATE] I forgot to mention the "odd games" issue as it relates to the more-than-two-teams head-to-head tie-breaker. As written, the current odd games rule is a mess. I would clarify it with one simple change: head-to-head points should be judged by W% in those games, not by total points. That way, it doesn't matter if teams have played more or fewer games against the other tied teams (as occurs when two teams are division rivals and a third team is not). 
• If all tied teams are also tied in head-to-head points W%, move on to the next (fourth) tie-breaker.
• If some but not all of the teams are tied in head-to-head-to-head points W%, the teams that are tied in head-to-head points W% repeat (do a second round of) the head-to-head tie-breaker, recalculating for only those teams that are still tied. 
• Example #1: Team A, Team B, Team C and Team D are tied in W%, total points and wins. The head-to-head tiebreaker is applied. Team A has a W% of .600. Team B and C are at .500; Team D .400. Team A gets the 1st seed, Team D gets the fourth seed; the head-to-head tie-breaker is repeated for Teams B and C, recalculating for only Teams B and C (removing games with A and D). If they are still tied, proceed to the next tie-breaker for those two teams only. Teams A and D have been awarded their seeds and Teams B and C proceed to the next tie-breaker. 
• Example #2: Team A, Team B, Team C and Team D are tied in W%, total points and wins. The head-to-head tiebreaker is applied.  Team A has a W% of .600; Team B, C and D all are at .500. Team A gets the first seed, and the tie-breaker is repeated (a second round), recalculating for the remaining three (still tied) teams. The recalculation yields this result: Team B is at .550. Teams C and D .500. Team B is awarded the second seed (Team A got the first), and the tie-breaker is repeated (a third round), recalculating for only Teams C and D. If C and D are still tied, only C and D proceed to the next tie-breaker. 
• The fourth tie-breaker -- head-to-head goal-differential -- is applied with the same logic as head-to-head points.
• [UPDATE] To account for "odd games", goal-differential figures are converted to goal-differential per game (i.e. GFA - GAA). 
• After a head-to-head goal-differential tie-breaker is applied, any teams that are tied in goal-differential (per game) repeat (do a second round of) the tie-breaker, recalculating for only the teams that are still tied. Teams that prevail are awarded the commensurate seeds. 
• The fifth tie-breaker -- divisional record -- is applied only if all tied teams are in the same division. Otherwise, the conference record is used. 
• The tenth tie-breaker cannot be a coin flip if more than two teams are tied at this point, so I'm going to suggest a pair of dice, although you could also do rock/paper/scissors. If rock/paper/scissors is the preferred method, I suggest televising it.
• However: if more than two teams are tied, and the 8th and 9th seeds are involved, a round-robin tournament will decide the seeds. Each tied team plays each of the other tied teams once. Seeds are determined by total points within the tournament. Any ties are resolved using the standard sequence of tie-breakers, using only the numbers (points, goals, etc.) from the tie-breaker tournament (i.e. the regular season is not included, only these tie-breaker games). 
• If, at the conclusion of this tournament, and after the application of all tie-breakers, we arrive back at the tenth tie-breaker, and the 8th seed is still in play, an additional single-elimination game is played. Or, if more than two teams are tied, another round-robin tournament is played. This process can be repeated until all ties are resolved or until the 8th seed is determined. 

Stanley Cup Finals

• Standard tie-breakers apply, with this exception: if the two teams are tied in W%, total points, wins, head-to-head points and head-to-head goals, the tie-breaker should be record against teams from the other conference. 
• If the teams have only played one game head-to-head in that season, the winner of that game gets home ice-advantage. (i.e. the old "odd games" rule does not eliminate this game from consideration.)