Pitch Counts

Maximum Pitches
League Age Pitcher per Day
17-18 105
13-16 95
11-12 85
9-10 75
7-8 50
Required Rest (14 and under)
Number or Pitches thrown Rest Days required
>65 4
51-65 3
36-50 2
21-35 1
<20 0

Rest Days is the number of days between games, so a team that plays Wednesday then Saturday would have 2 days rest and any pitcher who pitched more than 50 pitches would be ineligible to pitch on Saturday.
The Number of pitches thrown is kept by the official score keeper/pitch counter in AAA and above. The score keeper/pitch counter is the responsibility of the home team. In AA, teams keep their own pitch counts.
More pitching eligibility forms can be downloaded here.
The number of pitches is the first pitch to the last batter a pitcher faces.
For example, a pitcher has thrown 48 pitches. A new batter comes to the plate. Hist first pitch thrown is pitch #49. He goes on to have 5 more pitches before the batter is retired. If the manager removes him from the game, his pitch count would be #49, if he faces one more batter, it would be 55 (including the first pitch to the next batter).