In Ice Hockey there are several different types of penalties that teams can commit resulting in different levels of punishment. The five main types of penalties are Game Stop, Minor, Major, Game and Team & Misconduct. Apart from Game Stop penalties, all penalties will result in the offending player or players having to sit in the penalty box for the duration of the penalty causing their team to be shorthanded and be on what is called the "Penalty Kill" or PK whilst their opponents are on a "Power Play" or PP. The only exception to this is if a goaltender is penalised, then a player who was on the ice at the time must sit out the penalty for them.

When a penalty is commited it will be signaled and called by one of the officials using a certain hand signal or motion depending on the penalty that has been committed.

Below is a short and fun video showing some of the most common signals used.

Game Stop

Game Stop penalties are extremely minor infractions in the game where no player is required to sit out and the only punishment is a faceoff.
Here are the most common Game Stop offences:
Icing:When a player shoots the puck from their half of the rink over the opposing goal line. This results in a faceoff in the offending team's defensive zone. The only time Icing won't be called is if a team is on the Penalty Kill.
Offside:When either an attacking player enters the attacking zone before the puck on a drive or if the puck leaves the attacking they haven't exited the zone before it re-enters. This will result in a faceoff in the neutral zone by the defending team's blue line.

Minor

Minor Penalties are the least severe penalties. They are minor or accidental infractions. They usually result in the offending player being in the box for two minutes however some minors can be doubled if multiple offences happen at the same time or if the offence is deemed worthy of a "Double Minor".
Here is a list of the most common Minor penalties:
Tripping: When a player uses their stick or part of their body to trip an opponent.
Hooking: When a player uses their stick as a hook to slow down or impede an opponent.
Cross-Checking When a player hits an opponent with the stick when both their hand and none of the stick is touching the ice.
Slashing: When a player repeatedly swings the stick at an opponent and makes no contact with the puck.
Delay Of The Game: When a player stalls the game. This is usually by either holding the puck in their hand or playing the puck straight out of bounds during a clearance without the puck making contact with anything on its way out (another player or the plexiglass around the rink). It can also occur if the goaltender takes control of the puck behind his goalline outside of the designated area known as the "trapezoid"
(see Diagram for more clarification).
High Sticking: When a player makes contact with the opponent when their stick is over shoulder height. If the player draws blood, the penalty will be deemed a Double Minor and they will have to sit out for four minutes, if it is deemed to be deliberate and/ or malicious it can be upgraded to a Major or even Game penalty.
Roughing: Whan a player shoves or pushes an opponent after the whistle or away from the play.
interference: When a player impeeds an opponent who doesn't have the puck or impeeds any action from the bench like substitutions.
Holding: When a player holds an opponent's body or equipment usually to stop them from advancing the play.

Major

Major Penalties are deemed severe penalties. They are serious and deliberate infractions. They usually result in the offending player being in the box for five minutes.
Here is a list of the most common Major penalties:
Fighting: Fighting is when two players (usually on opposing teams) will drop their gloves and proceed to fight each other. Though there are no set rules for how they must go, it is most common for them to grab the front of their opponent's shirt whilst punching with the other hand. A fight ends when one participant touches the ice either by taking a knee or being wrestled to the ground. Both participants will usually receive a five minutes penalty but neither team will be down a player. The player who started the fight may receive two minutes Minor penalty for Instigation but this isn't always the case.
Boarding: When a player checks an opposing player straight into the 1.22 meter high boards surrounding the rink and not the plexiglass.
Elbows, Heads and Knees: When a player deliberately strikes another player with their Elbows or Knee or Headbutts them. Each of these can be upgraded to Game penalties if it is believed that the intent was to injure the player.
Charging: When a player takes more than three strides or performs a jump before hitting an opponent.
Repeat Offending: A player can be given a Major penalty if they are repeatedly called for minor penalties throughout a game. The number is up to the officials in charge but it is common that a 4th Minor penalty from a player in a game will be escalated to a Major.

Game

Game Penalties are the most serious and severe penalties. They are serious, deliberate infractions where it is believed the intent was to injure the opposing player and are commonly escalated from another Minor or Major penalty. They result in the offending player being ejected from the game meaning they will play no further part in the game. They usually also result in their team having a player sit the original penalty.
Here is a list of the most common Game penalties:
Spearing: When a player stabs an opponent with the stick blade.
Grabbing The Face Mask: When a player grabs and holds either the face visor or mask of an opposing player.
Goaltender Using The Blocker To Head: When a goaltender uses the protective blocker (found o the hand they use their stick with) to strike a player either in the face or head.
Check To The Head: When a player performs a check but makes full contact with the head of the checked player instead of the body.
Escalated Penalties: When a Minor or Major penalty is escalated to a Game penalty due to intent and/or severity.

Team & Misconduct

Team and Misconduct penalties are infractions that are usually committed outside of the actual game itself and commonly committed after the whistle and during line changes.
Here are a list of the most common Team & Misconduct penalties:
Too Many Men On the Ice: This is when a team will have too many active players on the ice at one time. This is usually due to a mix-up during a line change. This results in a two minutes Minor penalty where one of the players that were on the ice at the time sits out the penalty.
Abuse Of An Official: This is when either a player or coach is deemed to have used abusive language, remarks or actions towards an official. Depending on the severity of the abuse it will result in either a Minor, Major or even Game penalty being called on the offending player or the team.
Unsportsman-Like Conduct: This is similar to an "Abuse Of An Official" penalty but the actions are usually directed at either an opposing player, teammate or fan. Again depending on the severity Minor, Major and even Game penalties can be called against the offending player and/ or team.