If you're talking MLB, then there is no rule. For example the Yankees just pitched CC Sabathia on three days rest, if they wanted to they could start him tomorrow for game 5 of the 2009 World Series. But that would probably be extremely unwise.
Pitcher's rest is about saving that pitcher's arm, as the more tired or overworked the arm, the more prone the pitcher becomes to injuries. Typically 4-5 days of rest or a pitcher has one start roughly once a week as a general rule of thumb, hence your 4-5 starting rotation.
Again no rule exists and say the Phillies win game 5 behind Cliff Lee, and say Lee goes 6 innings and throws 50 pitches. Then if the Phillies need to call on him in game 5, the may just do so for 5 innings. It's rare but has been done before. It would be a suprise to see him at least come out of the bullpen if the above scenario happens.
For pitch rest in other leagues, Little League for example: The days vary by the number of pitches thrown by that pitcher. Example: If Johnny pitches on Saturday and throws 60 pitches, then he needs one calendar day of rest, so if he has a game on Tuesday he's eligible to pitch again, but not Sunday. I believe LL (12/13 and under) just added a pitch count rule of a pitcher can throw a max of 80/85 pitches. This is a safety measure to prevent injury and save the kids arm.
hope that helps.
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It depends on the league. Usually if its a new pitcher he gets 8 pitches. If the pitcher is coming back in for the next inning he usually gets 5 pitches (the total pitches to warm includes a throw-down by the catcher to 2nd base on the last pitch of the warm up)
There are no rules in Baseball on how often a pitcher can pitch. The safety and value of the pitcher's arm constitutes how often a pitcher can pitch.
Back in the older days pitchers pitched 200 or even 300 pitches a game. This factor was a considerable safety risk. Now the manager and the pitching coach keep close eye on counts of how many pitches have been thrown. Around 100 pitches is when a pitcher usually gets pulled now. Managers are wise to how valuable their pitchers arms are and they try to do their best to let them play to at least the 6th or 7th inning before pulling them. Of course, if a pitcher is shutting out the other team, they'll let him stay in, IF he's okay.
It's up to the manager whether or not a pitcher will play in consecutive games. There are no rules that state how many games a pitcher can appear in. There have even been times where a pitcher will start one game, and then in the next game they will be called in as a reliever.
Technically, yes. In practice, nobody does. The most likely scenario for a pitcher to start on consecutive days would be for a knuckleball pitcher to do it. According to wikipedia, Tim Wakefield pitched on consecutive days at some point. Another (very unlikely) scenario would be a pitcher starting a game that is called of very shortly due to rain and then not requiring the usual 5 days of rest before returning to the mound. In that case though, managers would probably keep their rotations in order and have the pitchers continue to make their scheduled starts.