As a gay kid who was ten the year Madonna broke out, her influence on my life is something immeasurable. I realize I'm a living cliche saying this, but she spoke to something in my DNA, something in my little queer brain clicked whenever Lucky Star or Like A Virgin or especially Into the Groove came on MTV (same with anything off Prince's Purple Rain....jeez 1984 was an awesome time to be ten years old!)
As for being objective about her music catalogue, I think I can be, despite being an uber fan....her first album is pure 80's pop goodness....Holiday, Burning Up, Borderline, Lucky Star, Everybody, Physical Attraction, all great dance pop. Like A Virgin, on the other hand, is a damn chore to get through as an album...aside from the title track, Dress You Up and Material Girl, i find much of this album unlistenable (her other greatest hits from the LAV era, Into the Groove and Crazy for You, aren't even on the album) True Blue is a step up, but I don't think she produced a totally solid album till Like A Prayer. That was her first album I could listen to from start to finish, and still holds up. I think with Erotica, Madonna produced another great album, but the overtly sexual themes turned off all but her loyal queer audience. I know that Bedtime Stories is seen as her "comeback" after Erotica, but to me it is a boring as hell album, with a few decent tracks.
To me, "modern" Madonna began with Ray of Light, and I love that album to death to this day. I can listen to this one from start to finish, I think it is brilliant, and Music and Confessions are not far behind. She may not have as many pop singles as she once had, but listening to a Madonna album these days is not about skipping to that song you like anymore. They are complete experiences. Unlike Michael Jackson, she continued to produce music and push herself for the most part, at least until very recently.
I think she doesn't care that much about new music these days though. Hard Candy was fun, but lazy. Her video for Celebration was generic and boring. She cares more about touring (where the real $$ is) and Madonna the brand (like the Dolce and Gabana glasses and her Material Girls line at Macy's) But after 25 years, she fucking earned it. Elvis and Marilyn's images and brand name sell everything from toothpaste to beach towels these days, yet were too self destructive to financially benifit from their iconic status. Let Madonna do what they couldn't I say.
As for GaGa, I will say this...she is Madonna's true heir. Not Britney, Not Christina, not Nelly fuckin' Furtado. I await each new GaGa video with the same thrill that a new Madonna video would bring me when i was a kid. She is competing in an arena Madonna seems to not care as much about anymore, the world of music videos and pop singles. Let her pick up the slack.