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.
Ted Lindsay Award: This award was named the Lester B. Pearson Award, but was re-named mid-2010. It was awarded for the first time in 1972. It is awarded to the League's Most Valuable Player as voted by the NHL Players Association. The voting is held at the end of the regular season.
Avalanche links: Joe Sakic won in 2001.
Conn Smythe Trophy: Was first awarded in 1965, and is given ever year to the player that is most valuable to his team for the entirety of the post-season. It is awarded based on the votes of the Professional Hockey Writers' Association. It is given to the winner before the presentation of the Stanley Cup at the conclusion of the final Stanley Cup game.
If you have looked closely at the award, you will notice that it bares a resemblance to a hockey arena - the Maple Leaf Gardens to be exact. This is because the award is named after the former owner, GM and coach of the Leafs. The award has been given to a member of the losing team five times in its history. Another five time exception? Get your tin foil hats out: all but five winners have been Canadian. The non-Canadians have been: Brian Leetch, Tim Thomas, Evgeni Malkin, Nicklas Lidstrom and Henrik Zetterberg.
Avalanche links: Joe Sakic in 1996 and Patrick Roy in 2001.
Art Ross Trophy: This award got first awarded in the 1948. It is given to the player who leads the league in points every regular season.
Avalanche Links: Only one: Peter Forsberg in 2003.
Calder Memorial Trophy: This is the NHL's Rookie of the Year Award. The first time it was handed out was in 1938. Now, at the end of each regular season, the Professional Hockey Writers' Association vote on who they believe was the most proficient in their first year in the NHL.They rank their top five, then the top three are announced, the winner is named at the Awards ceremony. Originally a new Calder Trophy was presented to the winner each year, that is until Frank Calder died in 1943.
Interesting fact: Sergei Makarov won it as a 31 year old. After he won, the rules were changed so only players 26 and under may be considered for the award. Another stipulation is that the player cannot have played more than 25 games in any season, nor six games in any previous two seasons (in any major league). This is why Wayne Gretzky could not be nominated for the award, he had played for the WHA before making it into the NHL.
Quebec Nordiques Links: Peter Stastny in 1981 and Peter Forsberg in 1995.
Avalanche Links: Chris Drury in 1999.
James Norris Memorial Trophy: This is yet another award that is chosen by the Professional Hockey Writers' Association, who vote at the conclusion of the regular season. It is given annually to the defensman with the best all-around ability on the back end. This award has been around since 1954, and has been in the hands of 23 players during that time.
Avalanche links: There are none, although Raymond Bourque won several times as a Boston Bruin.