A team is overdue if the number of years since their last appearance is greater than the number of teams in their league. The table below lists all such teams as of now in no particular order. Once we get into 2012, the Indians will be 15 years from their last appearance.
Some are very overdue. Some not only have not been making it to the World Series, but they have been doing poorly otherwise, too. This may seem like alot of teams, but at the conclusion of the 1958 season, 11 of the 16 teams were overdue.
We have always had hapless teams. The Phillies went 35 years without a pennant before finally getting one in 1950 but then went another 30 years. The original Senators did not win one in their last 27 years in Washington. The St. Louis Browns went only once to the Series in over 50 years before moving to Baltimore. The White Sox went 40 years without one until 1959 and then went another 46 years.
It is probably hard to quantify "overdueness" over baseball's history to accurately assess how bad things are now. In the pre-1960 years, you could be overdue in just 8 years so it may not have felt so bad to the fans. Now it means a longer time period. Right now, it would take 7 years to clear out the back log of teams overdue and it would require all of the hapless teams to get in over this stretch (it does not seem likely).
The following table shows the teams that are at least half way to being overdue.