Critical Dissonance: This is especially true for their song "My Humps", which was savaged by critics but still managed to become exceedingly popular and even won the 2007 Grammy Award for "Best Pop Performance by a Duo or Group with Vocal", in addition to the music video winning a VMA for "Best Hip-Hop Music Video."
Incredibly enough, The E.N.D wasn't very well-received, but the album singles were.
Ear Worm: Hear any song by them, and it will play in your head all day long!
Ahem, 'BOOM BOOM.
'Where is the love? Where is the love?"
Face of the Band: Either Fergie or will.i.am. Good luck finding an average fan that knows the names of apl.de.ap and Taboo.note Allan Pineda Lindo and Jaime Gomez, respectively.
Germans Love David Hasselhoff: To Filipinos. Mainly because apl.de.ap is of Filipino descentnote Born to an African-American father who was an airman stationed at Clark Air Base (who left him shortly after birth) and a Filipina mother, which led him to produce a number of songs about the Philippines (Bebot and The APL Song, along with Take Me To The Philippines, a promotional song done in collaboration with the Department of Tourism).
Irony: The 2005 song 'Gone Going' is about an artist who used to write meaningful songs, and now produces shallow, meaningless songs about wealth and partying after making it big. Fast forward a few years, and the Black Eyed Peas can be described very similarly.
It's Popular, Now It Sucks: The group when comparing to before after adding Fergie to the lineup, which is when they switched to a more pop oriented sound and became more commercially successful.
I Am the Band: Will I Am's performance at the Silver Jubilee kind of confirmed this!
Moment of Awesome: The Peas' manager punching out Perez Hilton. There's also their performance at Super Bowl XLV, where they drop onto the stage from the ceiling.
Painful Rhyme: Their later albums are chock full of verses where every line rhymes words that end in either "-tion"/"-sion", "-ing" "-een", "-er", "-ay" or "-o". This leads to excruciating lines on The Beginning, such as "audio and visual, can't see me – invisible" and "this shit's money nigga this shit green / this shit's frightening – Hallowe'en."
Sampled Up: "Misirlou" by "Pump It" (Dick Daleis not amused), as well as Sexual Harassment's "I Need A Freak" by "My Humps". The latter of the two was the subject of a lawsuit that began even several years before the song's release due to the sample being used without authorization.
Values Dissonance: "Let's Get Retarded" was just about acceptable enough in the early 00s that although it had no chance of getting on radio, it didn't get too much backlash after they changed the title. If a band had released a song with that title these days, their career would die overnight.