Jeffrey Beckmann at BleacherReport presents a slideshow of the "50 Best Teams" not to win a World Series. Of the teams on this side of 1950, the 1996 Braves and 1962 Giants top the list. In fact, the 1960s Giants achieved the best overall MLB record during 1960s but played in only one Series. The 2010 Phillies rank highest among teams not winning the World Series failing even to reach the Series (prior to 1969, there were no playoffs other than the Series). In terms of wins and losses, the 2001 Mariners with a massive 116 wins failed to reach the WS. This year, both the best NL and AL regular season teams, the Phillies and Yankees, lost in the Division Series. On the flip side, since the institution of the Divisional Series round, some mediocre teams (measured by regular season success) have have pushed through to WS titles such as the 2006 Cardinals, who finished the season at 83-78.
What accounts for very good teams losing and average teams winning the Series? Most obviously, the random element of any given game or short series of games makes winning-losing subject to chance, even when one team has much better on average. Introducing additional short series layers into the playoffs only increases this influence. As Skip has studied based on betting lines, MLB has a greater per game variability than most professional sports.
Besides the randomness component, the mix of inputs that maximizes success over a best of 5 or 7 game series differs, to some extent, from the mix creating success over 162 games. The underlying "process" generating outcomes is different. This difference creates a decision-making tradeoff for teams in putting together rosters -- go for the best 162 game roster to create the best chance of making the playoffs or compose a roster of a team best suited to win in short-series playoffs? It's a very difficult tradeoff for GMs and managers because, after all, winning the WS is contingent on making the playoffs.
Here is where one could question the choices of teams such as the Phillies. A team built on four "ace"-level pitchers can mow down the competition during the regular season. The Phillies won 102 games, 6 better than the next best NL team. Yet, once in the playoffs, are four "aces" worth the implied tradeoff of the hitters/fielders/relievers given up to attain them? Many of the memorable teams of the past contained at most two "aces" (sometimes only one) along with another starter who excelled under pressure. The Dodgers come to mind with Koufax and Drysdale supported by Podres. On the other hand, 1996 Braves went the 4-ace (or near ace) path.