Most of the sweaters below are third sweaters that are currently in use. Some full time sweaters are included because of a drastic and favorable shift in color scheme/logo.
Note: these appear in a generally chronological order.
The New York Rangers introduced the "Lady Liberty" third sweater in 1996. I like it for its patriotic overtones and its nod to the Statue of Liberty, which is not only a cultural icon, but a defining element of the city. Something it can call its own. And it refrains from gaudiness that the bad sweaters were so full of.
Also, in 1996, the Buffalo Sabres made a significant change in their colors and their logo. Out with the "running buffalo" and the crossed sabres. Out with blue and gold (Let St. Louis have that). In with black and red. In with a new, more stylized logo. Only the head of the buffalo, looking pretty pissed. I'm not a fan of the third jersey, which they introduced in 2000 (with just the crossed sabres), but I do prefer the red in that one to the black in the Sabres home sweater. Anyway, this was a great change. The sweater is much better looking than the old ones.
In 1997, the Ottawa Senators introduced a third sweater with a more cartoon-ish version of the senator. The traditional look had the senator/spartan in profile, while this newer one has him looking right at us. In 1999, this look became the official "road color" jersey and they introduced a different third sweater. Of course the league designated "team color" as the home sweater for the 2003-04 season, making this one-time alternate sweater the official home sweater. I like it because it stays close to the traditional logo, and yet it makes it look more punk rock. Maybe I like it because it's red.
The Flames introduced a third sweater in 1998. A pretty big change from the flaming C logo, which they brought with them from Atlanta and modified. A horse with flames shooting out of its nostrils. Who'd want to fuck with that? Certainly a tribute the city's old west heritage and its world famous rodeo, the Calgary Stampede. As a side note, one thing that organization does which I think is very cool is that the alternate captains wear a flaming A miniature Altanta Flames logo.
For the 1999-2000 season, Dallas converted their alternate sweater into their "real" sweater. One odd thing about this is that the "white" jersey has a significant portion of the sweater that is actually team colored. I don't really like the sweater that much except that it pays homage to the team's Minnesota NorthStars roots. By the same token, the gigantic star on the sweater pays homage to the state of Texas. The Lone Star State. Please, please please do not let history repeat itself. I'd really hate to see their current third sweater become the full-time sweater.
Probably my favorite third sweater is the Edmonton Oilers sweater, which was designed by comic book guy Todd McFarlane ("Spawn"), who happens to be a part owner of the team. I like the ultra-modern industrialism of it. The five spokes of the gear symbolize the five Cups the team has won. I don't like the lace-up style, but that's just my preference. The logo is cool enough to make up for it.
While they don't wear one of my favorite sweaters, it's worth pointing to the history of the Penguins sweater. They entered the league in 1967, wearing powder blue and white (left). That's enough to bring tears of joy to my eyes. Throughout the '70s, the shade of blue got a little darker, and actually two-tone. Then, in 1980, the Pittsburgh Steelers won the Superbowl and the Pittsburgh Pirates won the World Series. The Penguins decided to change their color scheme mid-season and ditch the blue (middle) in favor of black and gold (right), which the Steelers and Pirates both wear. The Bruins raised a lot of hell, claiming that they had invented black and gold as a color scheme, but the league wasn't hearing it.
There are other sweaters that I like, but these stand out the most.