For a starting pitcher to throw a complete game (CG) is now a rarity.  Once upon a time however it was almost a standard. In their careers, Roger Clemens (active leader) has thrown 118 complete games, and Pedro Martinez 46. Cy Young threw 749 complete games! The feat was accomplished much more often for about 80% of major league baseball's 104 year history, but in the 1980's there was a noticeable decline. This begs the question, why the dramatic change?

I added the number of CG for the NL and AL leaders from each year since 1910 together and sorted by dacade.  Then I added the sum of those 10 numbers and found the average/league for each decade starting with 1910-1919.  For example, during that decade each league's CG leader (NL/AL) averaged 32.3 CG per season.
   
    Years       NL/AL CG Leader's Avg./Season
1920-1929:              28.4
1930-1939:              26.6
1940-1949:              23.9
1950-1959:              23.2
1960-1969:              21.6
1970-1979:              24.1
1980-1989:              16.8
1990-1999:              10.7
2000-2005:              7.4
2006:                       6.0
Baseball Reference

This shows how up until around the 1980's, very little change occured in the number of complete games thrown. After 1990, the numbers drop off considerably. Last year in 162 regular season games, Mets pitchers cumulatively threw 5 CG...and none had more than 1.

In a 1999 article for USA Today, Mike Dodd spoke with several former pitchers about why this may be.  Warren Spahn as quoted by Dodd:

"The quality of a pitcher isn't measured on wins and losses. It's take me to whatever inning."

"Baseball has made non-athletes out of the pitchers, unfortunately. Why would I want my son to be a pitcher, especially in the American League? You pitch once a week, they count the pitches, you don't get to hit, you don't get to run the bases. It takes all the fun out of the game."

Former Mets pitcher Tom Seaver (231 career CG) in the same article:

"Organizations want to protect players without understanding the higher degree of excellence you can demand from them."

Before the days of blockbuster, guaranteed contracts, unless they were a well established major league talent, pitchers were fighting for their baseball lives when they took the hill. To not put it all out on the field might mean they would soon be giving it their all in the minors or even be dropped from the team.  In addition, organizations are paying way too much money right now to see their investment spend the year on the DL, so managers pull a pitcher from the game at the first sign of his tiring.

Also, with an emerged emphasis on the closer role and deepened bullpens, starters aren't required to go all nine innings anymore. It doesn't make sense to pay a closer millions of dollars to pitch only when a starter gets too tired to finish the game.

Mike Scoscia agrees:

"I don't know if it's ever going to get back to just letting a starter who gets a little tired win or lose a game in the eighth or ninth inning when you have the caliber of closers that are out there on a lot of teams and bullpens" he said.

I have to agree with this strategy as well.  Although I wish players today were tougher and more determined to prove their worth rather than just earn their money, the game has changed. As a fan, I couldn't bear to see a pitcher the Mets paid $20 million for go down because Willie decided to keep him in the game after he seemed to be tiring.

Placing too much pressure on a pitcher to throw a complete game also places additional strain on his arm.  The complete game has been phased out of a pitcher's mentality and out of their endurance level. It is similar to the evolutionary theory of natural selection if you are familiar with it.  Pitchers aren't conditioned to be able to throw that many innings anymore because the crutch of having a reliever/closer is always there to fall back on.  This has made the starting pitcher into a weaker breed of what it once was. Less is expected from them, so they expect less from themselves and demand less from their arms.  This probably helps their career longevity however.

I was asked if a team's roster size used to be smaller therefore creating the need for a pitcher to throw more innings. Or perhaps less pitchers occupied roster spots which would have a similar effect.  However it seems that this is not true:

"In 1910, a new scheme was instituted, with teams being allowed to keep as many as 40 players under control during the offseason and the early and late parts of the season. During the heart of the season, though, teams had to reduce their active rosters to 25 players. Beginning in 1957, teams were required to reduce their active rosters to 28 players by opening day, with the final reduction to 25 players coming 30 days later. Starting in 1968, the 25 man limit was in effect from opening day, although teams were allowed to carry 40 players after August 31."

In fact during the post-WWII era, accommodations were made to allow more than 40 men to be on a roster for a while. Also, even though more pitchers seem to be used today, a similar number of roster spots were held by pitchers in the formative years of the league when compared to today. On top of that, after 1961 the season was lengthened from 154 to 162 games which should have allowed for more CG. Baseball-Almanac

In short, the complete game will continue to become more and more endangered. Throwing a complete game is so rare now that when it occurs it is sometimes a fan's initial reaction to think "why didn't they take him out and just let the closer finish the game?"  Fully expect this to trend to continue.  Soon, if not already, the "CG" statistic will become a meaningless relic and will find itself on the same list as the Dodo Bird.  I give a pitcher kudos for hurling a complete game, but the opportunity to do so is becoming increasingly fewer and farther between.