One of Martin Brodeur's strengths is puckhandling. It is difficult to evaluate puckhandling since there are very few stats to go on, meaning we have to mostly rely on subjective judgment. There is no consensus on the subject, as shown in this HF Boards thread, where a number of Brodeur fans claim he is the greatest puckhandler ever, while others disagree, arguing that Brodeur is not even the best in the game today, surpassed by others like Marty Turco and Rick DiPietro. Given that there seems to be substantial agreement on those three as the best in the league, I will focus mainly on those three in the following analysis.
How can we try to analyze puckhandling? Probably the most obvious place to start is with the scoring numbers, goals and assists. Brodeur is famous for scoring a goal in the playoffs, but goalie goals are obviously very rare, as are goalie assists. This year, Turco had 4 assists to lead all goalies. DiPietro had 2, while Brodeur had just one. However, one season can be a bit fluky - some of the goalies who beat out both DiPietro and Brodeur in terms of assists include Vesa Toskala, John Grahame, Dwayne Roloson, Olaf Kolzig, Marc-Andre Fleury, and Johan Holmqvist, none of whom are particularly well-known for their puckhandling.
Looking back a few years to compare Turco and Brodeur can give perhaps a better comparison. In the last 4 seasons, Marty Turco has 10 assists to Brodeur's four. There were a number of goalies who also outscored Brodeur, many of them not known for puckhandling, like, for example, Roberto Luongo. Consistently piling up assists may be evidence of some puckhandling ability, but I think it is a poor measure because of the luck factor. Sometimes a goalie will get a second assist just for setting it up for one of their defencemen, because a teammate makes a superb play. Also, assists do not measure how well a goalie makes the easy plays, just how likely they are to connect on a home-run pass.
A statistic that can perhaps shed more light on the situation would be giveaways. The problem with giveaways, as with all of the NHL's real-time stats, are that scorers around the league vary substantially in how generous they are with awarding them. Therefore, we need to keep that in mind when interpreting the numbers.
Martin Brodeur's numbers came out as pretty solid - 33 giveaways in 78 games. However, his opponents had just 27 giveaways. There could be several reasons for this, such as the Devils having a less aggressive forecheck, but probably the main reason is that the scorers covering Brodeur seem to credit fewer giveaways. In the 4 games involving backup Scott Clemmensen, for example, there were just 2 giveaways for both teams (both charged to Clemmensen). Brodeur almost certainly handled the puck more often than most of his opponents, but his higher giveaway rate means he would have had to have made substantially more good plays just to break even with the goalies playing against him. It's certainly not unreasonable to suggest that he did, but the giveaway numbers don't seem to indicate that Brodeur is head and shoulders above his peers in this regard, as some observers claim.
Marty Turco had 31 giveaways in 63 games. His opponents had 44 giveaways, indicating that the scorers were more generous with the giveaways. This is reinforced by the games involving backup Mike Smith, as Smith had 12 giveaways and his opponents had 15 in 19 games. So although Turco had a slightly higher rate of giveaways per game, he did much better than his opponents, and when taking that into account it is likely that he outperformed Brodeur, at least in terms of taking care of the puck.
DiPietro is a very different story. He had an awful 75 giveaways in 61 games, compared to just 39 for his direct opponents. The scorers seemed to be pretty hard on the Islanders (backup Dunham had 12 giveaways in 15 games), but DiPietro's numbers are still very poor. His giveaways per game rate is almost triple Brodeur's, and he was charged with almost twice as many giveaways as his goaltending opponents. DiPietro may be able to shoot it hard, but he clearly needs to improve in terms of taking care of the puck, and it is doubtful that the positives make up for his very high error rate.
Martin Brodeur has the established reputation, but I believe the best puckhandling goaltender in the NHL is his successor on the competition committee, Marty Turco. This is from a combination of subjective observation and the above number-crunching. Turco is very aggressive with the puck, and his team's defensive style relies heavily on him playing the puck. Nevertheless, he still commits substantially fewer giveaways than his opposing goalies, and he led the NHL in assists. Brodeur was not charged with many giveaways either, but his opponents had even fewer, indicating that the official scorers watching the games were a little trigger-shy in handing out giveaways. Rick DiPietro is not close to as good as either of those two. He makes far too many mistakes, and isn't scoring enough points to make up for it.
This was a very superficial look at puckhandling, but objective analysis is very limited by the numbers available. I would need to collect more numbers to look at other goalies, as well as to get more of a league average benchmark to more properly analyze giveaway rates and possibly adjust for scorer bias in various cities. One other point that I hope to look at some time is whether some goalies reduce the number of hits taken by their teammates when they are in the game. For the time being, combining giveaways and assists with a subjective analysis of the goalie's play will have to suffice.