Awesome Music: "Stairway To Heaven" is considered by some to be the greatest rock song of all time. Coincidentally, others (even some who areLed Zeppelin fans) consider it to be the most overrated. Fans would nominate everything the band recorded between 1969-1975, with particular emphasis on IV and Physical Graffiti.
You could throw in Creator Backlash too; Plant reportedly said that he wished the band were remembered more for "Kashmir" than "Stairway".
Covered Up: Who remembers "When the Levee Breaks" by Memphis Minnie and Kansas Joe McCoy? Or "Dazed & Confused" by Jake Holmes? Or every other song they covered/plagiarised bits of?
Critical Dissonance: Although they were wildly popular with rock fans, Led Zeppelin was hated by music critics. Rolling Stone magazine gave negative reviews to every single Led Zeppelin album released during the 1970s (then, strangely, in 2006 they put Led Zeppelin on the cover of the magazine and called them the greatest rock band of all time).
Fan Nickname: "Led Zeppelin IV" -- or, somewhat less commonly, "Zoso" or "The Ruins" -- for the Led Zeppelin album with just the symbols on it.
First and Foremost: Quick, can you name a single band that's managed to cover up Led Zeppelin? Thought not.
Led Zeppelin. "I remember Robert Plant saying [they] were a cover band now because they cover all their own stuff." --Björn Ulvaeus, on why ABBA would never reform.
"When the Levees Break" after Hurricane Katrina hit New Orleans and...the levees broke. When the levee broke, the people of New Orleans didn't have any place to stay. The song is actually about the Great Mississippi River Flood of 1927, as it is a reworking of a Delta blues song from that era, but these days it's hard to associate the image of levees breaking with anything but Hurricane Katrina.
Also, Sandy Denny, who lent some vocals on IV--you know, the one with Stairway to Heaven on it?--died a few years later after falling down a flight of stairs.
There are entire communities of music lovers who think they are the most overblown, pretentious band in the history of music.
Also, amongst the Led Zeppelin fans, there are a good portion who despise "Stairway to Heaven" -- considering other songs from the band's catalogue to be far superior.
This was famously lampshaded in Wayne's World, with the music shop that Wayne and Garth like to visit carrying a strict "No Stairway To Heaven" policy for people interested in testing out instruments.
The Law of Fan Jackassery: Since the band's heyday is long gone, but the band is still widely well-regarded -- the fanbase is pretty much at the peak.
"All My Love" is a Grief Song that Robert Plant wrote after his five-year-old son died of a stomach virus.
Can also include: "Stairway To Heaven", "Over the Hills and Far Away", "Thank You", "Hey, Hey, What Can I Do", "That's The Way", "The Rain Song", "Tangerine", "Ten Years Gone", "Going To California", "Babe, I'm Gonna Leave You", "No Quarter", and "The Battle of Evermore".
The scenes from the Rockumentary film The Song Remains the Same that Robert Plant's children appear in can also bring one to tears -- when you watch how happy and playful young Karac is, and realize that his life will come to a tragic end in a couple of years.
Led Zeppelin was initially trashed by music critics, including Rolling Stone. There's also a brutal Melody Maker review of Led Zeppelin III that, for a while, seemed to be something of a Berserk Button for Jimmy Page. Now, of course, both publications have "revisited" those assessments.
The press in general was a Berserk Button for John Bonham. He once threw a fit at a journalist who claimed to be a fan.
Zeppelin Is Unheavy: Well, try finding one famous band that doesn't have this sort of thing. In particular John Bonham's drum beats. (Especially "When The Levee Breaks") His influence is so pervasive in modern rock that many younger listeners are legitimately baffled as to what's the big deal about him.
Imagine how the people who went to see them in '68, when they were going by The New Yardbirds, must have reacted. For illustrative purposes, here are the Yardbirds, and here's Zeppelin.
Double Subverted: When Jeff Beck joined The Yardbirds they were known as a heavy band (Beck being one of the first to really use distorted guitars. Just look at this clip from the film Blowup (which was during the short lived Page/Beck line-up), while never trashing instruments on stage (they did originally want The Who) it's still far from "light".