In Little League, a pitcher may pitch in consecutive games if 40 pitches or fewer pitches were delivered in the previous game. (Regulation VI - Pitchers (e) P. 35).

1-20 Pitches in a day, he/she needs no calendar days rest and may pitch in the next game.
21-40 Pitches in a day, he/she needs one calendar day of rest and may pitch in the next game.
41-60 Pitches in a day, he/she needs two calendar days of rest, and a a game.
61+ Pitches in a day, he/she needs three calendar days of rest, and a game.

Examples: 

If a player throws 65 pitches on Monday and the next game is Saturday.  The player cannot pitch in the game on Saturday.  Since the player needs 3 days rest and a game rest, he/she would not be able to pitch.  He/she has not fulfilled the 1 game off requirement.

Same example as above (65 pitches), but the team plays Monday, Wednesday and Friday.  The player may pitch in the Friday game.  The player observed the 3 days rest (Tuesday, Wednesday and Thursday) and the one game rest (Wednesday's game).  This player would be eligible to pitch in the Friday game.

Player throws 25 pitches.  Team plays Monday and Wednesday.  The player may pitch in the Wednesday hame.  He/She has observed the one day rest (Tuesday) and need not rest one game.  This player would not be eligible to pitch on a Tuesday game because they would not have met the one day rest requirement.

Player throws 15 pitches in a game.  The player may pitch in the next game regardless of when it is played.  They need not rest a day and they need not rest one game.