While pitchers back in the 50's and 60's would average about 100 pitches per start, they would go longer on 'good days' and shorter on 'bad days.' In other words, when the starter was pitching well, he would be allowed to go past 130 pitches. And if he wasn't, he'd rarely go beyond 70. In the modern game, managers often force starters to continue pitching, even when they're ineffective, and even when they are, won't let them go much past 110.
I'll let Keith Woolner sum up:
Pitchers in the 1950s came out of the game when their performance dictated it; pitchers today come out of the game when their workload dictates it.
Why is this the case?
There seem to be several reasons:
1. Specialization
What's happened to the long reliever in MLB? They're practically extinct. What used to be a vital cog for winning ballclubs has given way to more pitchers pitching fewer innings (e.g. the LOOGY and the 8th-inning guy). For example, Al Aceves, the closest the Yankees have to a long reliever, averaged less than two innings per appearance last year. Perhaps managers don't have enough confidence in said relievers to let the opposing batters see them more than once.
2. Offense
While pitchers are averaging about the same number of pitchers per start as they did in the past, they don't pitch as frequently (the five-man rotation began in the early 70's) or as efficiently. The DH, lower mound, smaller ballparks, smaller K-zone, juiced balls, PEDs and an appreciation for walks have all contributed to making life tougher on pitchers. While Sandy Koufax averaged 19 complete games per year (from 1961-66), CC Sabathia has never had more than 10 in any season. Though I'm not sure why this means managers have to force struggling starters to stay in the game; perhaps they feel a need to 'get their money's worth': since they won't let them go 130+ pitches on a good day, they need to get more on a bad day.
3. Longevity
There is certainly more thought and care put into extending pitchers' careers. It's not just 'what can you do this season?', but 'what can you do five years from now?' Managers and executives realize that taking precautions with pitchers can extend their careers (which is also sound fiscal management). And nowadays high-pitch games are seen as more detrimental than, say, more games at lower pitch-counts. (Two 100-pitch games are easier on the pitcher than one game of 50 and another of 150. Anyway, that's the thinking.)
Any other reasons I'm missing?
Slightly off topic...
In 1988 (the first year full league pitch data is available) we saw 134 pitches/game/team and 21708/year/team. And in 2009 we saw 147 pitches/game/team and 23814/year/team.
So 2009 teams threw about 2100 more pitches than 1988 teams (though nowadays it's spread out over slightly more pitchers). What's perhaps more interesting (than why is there such a difference between the usage of modern pitchers vs. 50 years ago) is why there is such a vast difference in only the last 20 years. The DH, lower mound and PEDs all existed in 1988, just as today. What could make for that 2100 pitch difference?