There are a number of different awards given every year. Some are to a team, but most are to honor individual efforts. Here is a list of the awards, what they are, some historical information on the trophy, and which Colorado Avalanche player, if any, won the award.
Vezina Trophy: The Vezina Trophy has always been an award for a goalie, however, there have been two ways to win it. Originally, it was awarded to "the goalkeeper(s) of the team allowing the fewest number of goals during the regular season". Now it is given to the best goalie, as judged by the general managers.
This award is named after George Veniza, a goaltender for the Montreal Canadiens from 1910 until 1925. He was an ironman goaltender. Appearing in 325 consecutive games, until he collapsed during a game in November 1925. He succumbed to tuberculosis a few months later.
Avalanche links: Although Patrick Roy won this award twice in his career, he never received the honor while in an Avalanche uniform. He won it both in 1989 and in 1990.
William M. Jennings Tophy: This award is also an award for goaltenders. It is now, what originally was the Vezina Trophy. That is, it is awarded to "the goalkeeper(s) having played a minimum of 25 games for the team with the fewest goals scored against". The reason for the change was because the Vezina often went to the "best" team, the team that allowed the fewest goals - and wasn't necessarily a representation of the goalies' efforts. So they introduces the William M. Jennings trophy to also reward the best defensive team. This is awarded most often to the goalie tandem.
Avalanche links: Patrick Roy won this award a stunning five times. Four of those times in the Canadiens uniform. In 2002 Roy won it in Avalanche gear, however, he played 63 games that year, so he was the only Colorado Avalanche goalie to receive the honor.
Lady Byng Memorial Trophy: The Lady Byng is awarded to the "player adjudged to have exhibited the best type of sportsmanship and gentlemanly conduct combined with a high standard of playing ability". This is another award voted on by the Professional Hockey Writers' Association.
There have been three different Lady Byng awards. The first time it was awarded in 1925 it was simply called the Lady Byng Award. In 1935 Frank Boucher received the award permanently after having received it seven times in eight years. The second trophy was awarded from 1936 until 1949 when Lady Byng died. That award was the retired and the third one, the Lady Byng Memorial trophy was introduced. If you are wondering where the first incarnation of the award is: it doesn't exist anymore. It was destroyed in a house fire.
Avalanche Links: Joe Sakic won in 2001.
Maurice "Rocket" Richard Trophy: The Rocket trophy is named after the great Montreal Canadien Maurice Richard. One of Richard's claims to fame was being the first NHL player to net 50 goals; he managed to do this in 50 games. Appropriately this trophy is given to "goal-scoring leader during the regular season". It was first handed out during the 1999 season. There are no tie-breakers when it comes to this trophy, because of this it is possible to have more than one winner in any give year. In fact, in 2004 the trophy was awarded to three players.
Avalanche Links: The current captain, Milan Hejduk, won in 2003. He is the only Avalanche player to earn this trophy.
Frank J. Selke Trophy: This award came into existence in 1978 to reward the "forward who best excels in the defensive aspects of the game". It is voted on by the Professional Hockey Writers' Association.
Avalanche Links: There are none.