Hartford Whalers in a walk.
The Whale logo, in particular on either the blue or white sweater, so that it's 3-color (white, green, and silver) instead of the white-only logo on the green sweater, is the gold standard of defunct teams, and is soooo much better than many current NHL logos.
I've always thought the Wings logo is the best in sports.
All the original 6 logos circa 1970s are iconic (exception: pre-1970's Leafs is better than ~1970-2016 Leafs), plus Buffalo's because if it's Whale-like in that it's logo incorporates the city too. St. Louis logo is another modern-era goodie.
If we're talking sweaters and not just logos, Chicago's black sweater version is truly snappy and special.
For defunct teams, I also liked the Nordique logo/igloo, especially with the fleur-de-lis midriff sweater.
Call me crazy, but I've always found the Canucks original logo and sweater color scheme pretty snappy. Similarly, (and bizzarly) the Coyote's "Picasso's Dog" version - but that's probably just me.
Many of the other logos are plain abysmal, IMO. Ducks have never got it right. Dallas too. Wild? Avalanche? Thrashers were a complete turd - if only Sherman could have burned that. I understand the desire for more complex modern logos, but the simplicity of the older ones allowed you to draw them on your school folders and notebooks.
NFL? I think there are two classic color schemes: Green Bay Packers bright yellow and green, and the Buffalo Bills classic red/white/blue. Standing Buffalo logo ca. 1960s-early '70s is by far better than any of the charging versions. Colts logo is iconic. Honorable mention to the Steelers black/yellow/white color scheme & half-logo.
Houston Oilers had a good color scheme and logo, as did the powder-blue-era Chargers.
Current Patriots logo looks like the US Postal Service symbol updated a couple decades ago. Most of the other NFL logos are pretty uninspiring too.