IG2EUS: Iron Maiden

The Irreverent Guide To Everything Under the Sun has this to say on the subject of Iron Maiden:

Iron Maiden are, perhaps, the greatest band ever made. They are certainly the greatest band ever that is not the Beatles.

Their genre is Heavy Metal. Not Thrash Metal or Speed Metal or Power Metal. Just Heavy Metal. They are bloody famous for their epic songs and awesome harmonies. They also have, in the form of singer Bruce Dickinson, the single greatest singer in the history of music, ever.

They have made 15 studio albums. Only bassist Steve Harris and guitarist Dave Murray have appeared on all 15. Oh, and Eddie. Eddie the Head is their mascot. He may or may not be an alien, zombie, cyborg, or all of the above.

History
There are two ways of dividing Iron Maiden history into four blocks.

Method 1:

• Pre-Bruce
• Iron Maiden (1980), Killers (1981)
• Classic Bruce
• The Number of the Beast (1982), Piece of Mind (1983), Powerslave (1984), Somewhere in Time (1986), Seventh Son of a Seventh Son (1988), No Prayer for the Dying (1990), Fear of the Dark (1992)
• Minus-Bruce
• The X-Factor (1995), Virtual XI (1998)
• Re-Bruce 
• Brave New World (2000), Dance of Death (2003), A Matter of Life and Death (2006), The Final Frontier (2010)

The main advantage to this method is that it tells you who's behind the microphone. The major disadvantage to this method is that it doesn't give you the slightest  indication what's going on behind the scenes.

Method 2:

• Early Days (1980-1982)
• Iron Maiden, Killers, The Number of the Beast
• The lineup during this era was constantly shifting, adding guitarist Adrian Smith in 1981, singer Bruce Dickinson in 1982, and finally drummer Nicko McBrain in 1983.  None of these albums are exactly masterpieces, but by Beast it's clear that the band has found its footing.
• Classic Era (1983-1988)
• Piece of Mind, Powerslave, Somewhere in Time, Seventh Son of a Seventh Son
• With Bruce now freed from a provision of his previous band's contract and able to write songs, and Adrian firmly entrenched as a powerhouse songwriter, the band pumps out four absolutely essential albums.  Or rather, three: Somewhere in Time suffers from synthesizeritis (and was doomed to failure seeing as it was a lighter offering the year Metallica did Master of Puppets).
• Janick Era (1989-1998)
• No Prayer for the Dying, Fear of the Dark, The X-Factor, Virtual XI
• Adrian Smith quits.  Not to knock his abilities as a guitarist, but his songwriting abilities are missed more. Two albums later, Bruce Dickinson quits. Not to knock his songwriting abilities, but his singing abilities are missed more.
• Six-Piece (1999-Present)
• Brave New World, Dance of Death, A Matter of Life and Death, The Final Frontier
• Steve Harris decides to put the band's best interests ahead of any personal beef he has with Bruce Dickinson. Bruce agrees to return only if Adrian does as well. Adrian, who is old friends with his replacement, Janick Gers, refuses to return if it means Janick has to go, so the band becomes a six-piece with Janick continuing to play a number of Adrian's solos live.

Notable Songs
You should know the following Iron Maiden songs by heart:

• Iron Maiden
• "Phantom of the Opera." If you added this song to the production quality of AC/DC's Back in Black, out the same year, you'd have the formula for the next half-decade of music.
• "Remember Tomorrow"
• "Iron Maiden." It's one verse and a chorus. First major use of the twin-guitar harmonies.
• Killers 
• "Wrathchild"
• The Number of the Beast
• "The Number of the Beast." Actually probably about a nightmare Steve Harris had. Has the exact same plot as a Nathanial Hawthorne short story. So, not exactly satanic. 
• "Hallowed be Thy Name." The. Greatest. Song. Ever.
• Piece of Mind 
• "Revelations"
• "The Trooper." Easily the most famous use of the twin-guitar harmonies. Based on Alfred Tennyson's "The Charge of the Light Brigade."
• Powerslave
• "Aces High"
• "2 Minutes to Midnight." The intro riff was borrowed by Adrian Smith from this song... written by his future replacement, Janick Gers. Small world.
• "Powerslave"
• "Rime of the Ancient Mariner." Thirteen and a half minutes of your life you won't regret wasting. Also, you'll never mis-quote "nor any drop to drink" again.
• Somewhere in Time
• "Wasted Years." Adrian Smith's masterpiece.
• "Alexander the Great"
  
• Seventh Son of a Seventh Son
• "Can I Play With Madness"
• "The Evil That Men Do"
• Fear of the Dark
• "Fear of the Dark." Do not go to an Iron Maiden concert if you haven't memorized the guitar fills. Everyone will be singing along to them. Yes, the guitar parts.
• Brave New World
• "The Wicker Man"
• "Brave New World"
• Dance of Death
• "No More Lies"