Can't say I was ever a big Bee Gees fan. When I was young they were already in "phase 2" of their career; "The Disco Years". They started their career as a 60's pop group, lighter than the Beatles, more in the vein of British bands like , say, the Zombies maybe?
There would actually be a "Phase 3", the difficult "post disco" years; trying to escape the shadow of the disco years. They were never more famous than the disco years but being associated with that genre became a bit of an albatross for them. The 80's were some leaner years for the band.
In 1997 they were inducted into the Rock n Roll Hall of Fame. By this time they had become respected elder statesman for their full body of work and continued to write some catchy songs.
Newer bands like the Smithereens, The Posies and musician Jon Brion have proclaimed their admiration for the band's early work and many of their songs have been covered.
Here's 5 good Bee Gees tunes:
"I Gotta Get a Message to You"
the Wallflowers did an awesome version of this one
"I Started a Joke"
"to Love Somebody"
Of course this one always makes me think of Jimmy Fallon's hilarious "Barry Gibb Show" skit.
This song has the right amount of R&B influence , they would later over do it with the disco stuff , in my opinion.
"Nights on Broadway"
They continued to write some decent newer stuff. Their final album "This is where I came in" has kind of a modern rock sound. If Matchbox 20 or Train, etc. would have done some of these songs they may have been hits.
"This is Where I Came in"
bonus: an acoustic medley they performed live on the Howard Stern show
for further musical recommendations by the band read this one from USA Today. You can tell by Edna's choices, she is a real fan. Lots of deep cuts
Robin Gibb: Recommended listening