Her cultural impact. Bad Romance. Poker Face. BTW. How she became one of the best touring artists of all time in just 4 years, something other girls that have been for 10+ years could never do. The GP associate her with over-the-top performances, and her tour receipts prove it. The meat dress. She's basically a gay icon and BTW will forever be a staple of LGBT.
Of course the pressed will try to deny her impact.
Lady Gaga most "iconic" look is this. For the simple fact that it's from her biggest hit and there are like a million Halloween stores that sell this leotard.
And of course that makes the song "iconic". Her biggest single? I'm not sure. But it's been sampled in hip hop, covered, etc.
And last but not least, the often joked about Meat Dress.
And I guess the Bad Romance video/song too. But personally I don't consider it "iconic".
Hair bow
Glasses with screens
Custom piano's (like the one on fire) + Keytar
Paparazzi @ VMA's
Meat dress
Prosthetics on her body
Gaga as a motor cycle
Vessel
just to give you an idea of what to start the list with
Poker Face
Bad Romance
Bad Romance video
Telephone collaboration with Beyoncé
Born This Way (1000th single to go #1, importance due to its LGBT-friendly lyrics)
Meat Dress
2009 VMAs Performance
Her clothing is iconic/instantly recognizable. Whenever her contemporaries or anyone dresses even the slightest bit "weird", people compare them to Gaga.
I suppose she has a few iconic songs but I don't really see how a song itself can be iconic/instantly recognizable. It's all about the visuals that accompany the song that determines its icon status.
Her hairbow is iconic.
If you don't count this as clothing, her shoes. She single-handedly influenced the shoe industry to start making heel-less shoes on a commercial scale. Yes, heel-less shoes existed before Gaga, but she made them popular.
I suppose one could argue her gay rights advocacy is iconic, if that's even possible. I think a lot of people in the pop culture mainstream connect Gaga with the gay rights movement.