If off-side and icing are the traffic tickets of hockey, then minor and major penalties are the misdemeanors and felonies. For infractions like tripping, slashing, roughing, charging, high-sticking, and the always embarrassing too-many-men-on-the-ice, a player must sit out for two minutes in the penalty box, while his team plays on with one fewer skater than its opponent. If that team takes another penalty, then it'll have to make do with only three skaters to the other team's five (goalies are not considers "skaters"). However, additional penalties can't reduce the number of skaters on the ice below three -- any further penalties are staggered so that a new one begins as soon as one ends. If a penalty is called on a goalie, another player sits out the two minutes in his place.
When a team takes a penalty, the other team goes on the power play, which means it has more players on the ice than the opposing team. If the team on the power play scores a goal before the two minutes are up, the penalty ends automatically.
Coincidental penalties happen when a player on each team is called for an infraction at the same time. They both go to the penalty box, and the teams play with four skaters apiece. Goals scored during four-on-four play do not end the penalties in this situation.
The most serious rules violations result in major penalties, and possibly fines and suspensions. A major penalty lasts for five minutes, and it doesn't end if the team on the power play scores. A player who drops his gloves and throws punches will always get a major penalty, though a fighting major is usually offset by a penalty to the other team, since it takes two to have a fight. When two players on opposing teams get major penalties, five players remain on the ice per side. Major penalties can also be called on other infractions that are deemed more severe by the referees. Elbowing and high-sticking can be called as major penalties, particularly if there was an apparent intent to injure the other player. In this situation, league officials will review video tape of the incident after the game, and might add a fine and a suspension for the offending player.