RealGM

60s: 60-61 Hawks
70s: 70-71 Bullets
80s: 86-87 Hawks
90s: 91-92 Bulls and 95-96 Sonics
2000s: 00-01 76ers and 05-07 baby Bulls
2010s: 2010-11 Bulls

1960s: 1966/67 Sixers
1970s: 1978/79 Sonics
1980s: 1983/84 Jazz
1990s: 1998/99 Spurs
2000s: 2006/07 Spurs
2010s: 2012/13 Spurs

I was born in 1987, so everything before the 90s is based on reading and Youtube videos.

60s: no idea to be honest
70s: 76-77 Blazers and 78-79 Sonics
80s: One of the mid 80s Bucks teams
90s: 95-96 Sonics
2000s: 02-03 Mavs
2010s: 10-11 Mavs
2020 so far: last years Nuggets (before the Murray injury)

1960s: 1966/67 Sixers
1970s: 1971/72 Lakers
1980s: 1988/89 Pistons
1990s: 1992/93 Bulls
2000s: 2000/2001 Lakers
2010s: 2012/13 Heat

1970s : 1976-77 Blazers
1980s: 1987-88 Blazers
1990s : 1991-92 Blazers
2000s : 2008-09 Blazers
2010s : 2018-19 Blazers
2020s: 2019-20 Blazers

1970s:
74-75 Spirits
74-75 Q's
75-76 Braves
76-77 76ers
76-77 Pistons
76-77 Bulls
77-78 Jazz

1980s
79-80 Clippers
81-82 Warriors
82-83 Sonics
84-85 Jazz
84-85 Cavs
85-86 Warriors

1990s
90-91 Sonics
92-93 T-Wolves
94-95 Nets
96-97 Blazers

2010s
09-10 Grizzlies
10-11 Grizzlies
17-18 Pelicans
18-19 Spurs

2020s
21-22 Bulls

Bulls for each decade

Setting aside my Mavs of course....

Showtime(hey I was a kid)
Reggie/Detlef/Davis Brothers Pacers
More Cowbell Kings
PG/West/Hill/Hibbert Pacers
Grit and Grind
no team stands out in more recent years

1980's

showtime lakers

83 sixers

bird celtics

1990's

jordan bulls, both versions

hakeem rockets ring teams

penny and shaq orlando

late 90's jazz

2000's

duncan spurs 2002-2007

big 3 celtics

08-10 cavs for lebron

nash suns


2010's

2012-2016 thunder + 2017 and 2018 thunder

2013 nuggets

2013-2014 pacers

2014-2015 clippers

2012-2013 heat

2015-2017 cavs

2020's

2021-2022 bucks

2020 lakers

90's - run tmc / shaq and penny magic
00's shaq lakers / we believe warriors
10's kerr's warriors
20's current warriors

Not considering any core that won titles or made Finals.Limiting myself to teams I remember watching

Teens: Clippers
Aughts: Blazers
90s: Zo era Hornets

Not picking the Bulls for the exercise

80s: 87 Lakers
90s: 95 Rockets
00s: 08 Celtics
10s: 16 Warriors
20s: 22 Warriors

1995 Rockets
2008 Celtics
2014 Spurs
I guess the 2020 Nuggets? No one has really taken this spot.

Early to late 50s: Warriors
Late 50s to early 60s: Hawks
60s: Celtics
70s: (hometown Bullets of course but otherwise) Kentucky Colonels, Sonics
80s: Bucks
90s: Whoever was playing Chicago; seriously, Jazz, Cavs
00s: Spurs
10s: Warriors
20s so far: Bucks

1950s - 1955 Celtics
1960s - 1969 Knicks post-Debusschere trade
1970s - 1975 Warriors
1980s - 1983 Bucks
1990s - 1995 Magic
2000s - 2001 Lakers
2010s - 2011 Knicks pre-Carmelo trade
2020s - 2022 New Orleans Pelicans

70s-Bucks
80s-Lakers
90s-Magic
00s-Webber's Kings/Kobe's Lakers
10s-Clippers/Heat
20s-n/a

early 50s: kinda want to say the Lakers (the best of the best); though the teams I've seen the most of [which is to say about 1.75 full games so far] are the Knicks and Pistons (between them I like the Knicks squad).
late 50s: Celtics

60s: Celtics. Have taken a lot of interest in them over the years. I have a lot of respect for Russell, not just as a player, but as an individual (civil rights involvement, etc). And they're simply intriguing for the way in which they dominated.

early 70s: Knicks.
Bucks and Celtics are kinda cool, too.....but definitely the Red Holzman Knicks with Frazier, Reed, Bradley, love watching Dave DeBusschere's energy; I always liked watching Dick Barnett, too. Those teams were beautiful.
late 70s: Bullets become intriguing by middle of the decade; Suns are kinda fun. The '77 Blazers are fun to watch. Lakers are interesting just in how much of a one-man show they were (Kareem was just phenomenal). Don't have a firm fav for those years.

early 80s: probably Lakers, though Celtics also fun. '83 Sixers are interesting and cool just for how dominant they were.
late 80s: Well, at the time I was a Jordanite, so--->Bulls. Retrospectively, the Pistons [a team I HATED at the time, because they were Chicago's nemesis] are really interesting. And the Celtics again, very entertaining; obviously the ShowTime Lakers as well.

early 90s: Bulls. I appreciated [some more lately] teams like the Suns, Cavs, Knicks, and Blazers of that era too.
late 90s: Bulls [certainly was the case at the time]. Utah has grown on me with age. Seattle was entertaining, too.

early 00s: idk. I was wiling away the years still cheering for the Bulls, so suppose them. There were a lot of hard years as a Bulls fan after the dynasty completely exploded. Years at the bottom of the league. At the time I had tribalistic notion that once you picked a franchise you had to stick with it forever, no matter what.
These days I'm content to cheer for whichever players/teams capture my interest, simply as a fan of basketball.
late 00s: Suns. I moved to Phoenix in '04, lived there for four years. What a fantastic time to be a basketball fan in Phoenix. Have since developed a grudging appreciation [even affection] for the Spurs, too. Also enjoyed the Cavs a lot during that time period.

early 10s: I kinda followed LeBron, so I suppose the Heat. Also like the Clippers. Again liked the Spurs, and their '14 squad in particular was just beautiful to watch.
late 10s: Jazz. It was toward the end of the '15 season that I took notice of this young Rudy Gobert, who seemed to facilitate a total mid-season turnaround on their defense once inserted as a starter, rejuvinating the team. They'd gone 6-19 in their first 25, and were just 17-33 shortly before the All-Star break. Then they closed the season 21-11. I told my dad before the following season "this Gobert will be DPOY someday". One of the few instances I was right. I've been a Jazz fan ever since.
Also enjoyed the Cavs and the Raptors during this time. Golden State was fun, and you can't help but to like Steph Curry, really.......but I was frankly annoyed with them for making most years a foregone conclusion. I mean, take '17 for example: who the hell could actually beat that squad? No one; ever. The only hope for ANYONE else was a malicious hope: that one of GS's big three [four] would get injured.

early 20s: Jazz.


EDIT: I see I didn't quite do this as OP intended. Oh well..