The Mighty Avengers (Marvel)
The Authority (Wildstorm)
The Ultimates (Marvel) early issues with Millar
Fantastic Four (Marvel) Thomas, Byrne, Brubaker
Rising Stars (Wildstorm) - anything with Staczynski.
JLA (DC) Meltzer, Shooter, O'Neil (not sure what year)
The Defenders (Marvel) early 70's Wein, Buscema
X-Men (Marvel) Claremont 70's-80's issues
Titans (DC) Wolfman, Perez
The Boys (Dynamite) whoever is doing the series now

I went with the writers since I have so many things off the top of my head.

The Midnight Sons (not really superheroes, but they are a group), The Avengers, and of course, X-Men. I also like some of the early superhero team-ups.

The Fantastic Four from Marvel hands down. The first Galactus tale where Reed obtains the Ultimate Nullifier is probably the best tale. The first encounter with the Frightful Four was also pretty good. I was never a big X-Men or Avengers fan so I didn't consider either of those groups. For DC it would be the Batman/Superman team-ups in Worlds Finest. You can't match the two best icons teamed together matching Batman's brains with Superman's powers. Probably when they fought the Joker/Luthor team were their best tales.

From DC I've always had a soft spot for the Legion of Super-Heroes, despite them being changed so darn much since the Silver Age.

As a kid, I loved the rampant robots that even Superboy could not handle and when Triplicate Girl died, turning into Duo Damsel, I was crushed!

For modern comics, I really liked the Blackest Night and the Green Lantern Corps, much better written than earlier Green Lantern stories with Kyle Rayner. Hal Jordan was much more what I originally liked about the character and the dead coming to life, even cancelled comics coming back to life, was a fun read.

Finally on the Marvel side, I'd have to say I really like the Fantastic Four, even more so than X-Men or Avengers. Defenders were fun, Invaders were boring.

Best stories for the FF include for me the coming of Galactus and the Silver Surfer from back in the day. More recently I did enjoy the death of Torch storyline, but they left it wide open on bringing him back. I still don't get why he didn't just go Nova at the gates and wipe out his enemies rather than let himself get overwhelmed. Maybe I need to read it again, LOL.

Great question.