Finger on Lips

When a song contains swearing and the music video involves the band or singer singing, they will sometimes put their finger on their lips and not say anything when it comes to the offending word.

Examples of Finger on Lips include:

Pop

Gwen Stefani "Hollaback Girl" - a number of times.
Beyoncé is doing this in her and Gaga's video for "Telephone"

Rock

In Third Eye Blind's "Semi-Charmed Life", the whole song is about crystal meth, but the drug is only mentioned by name once. When it's mentioned in the video, the lead singer covers his mouth with his hand to prevent uncensored lip-reading.
Panic! at the Disco's video for "I Write Sins, Not Tragedies" at the word "whore". Complete with a "shh" sound. Later, Brendon Urie very blatantly covers or makes a cross over his mouth when he's onscreen for the "goddamn", apparently in reference to the issue of taking God's name in vain.
Seether's "Fake It" video. Whenever Shaun Morgan sings "you're such a fuckin' hypocrite", one of the scantily-clad women surrounding him covers his mouth and feigns shock.
The Bloodhound Gang's "Fire Water Burn" is an interesting example. In the video, when you hear Jimmy Pop sing "Burn motherfucker, burn," the video shows him making a strained face instead of pronouncing "fucker". In the censored version of the song, "fucker" is replaced with a donkey's bray.
In the music video for Theory of a Dead Man's "Hate My Life", when the construction worker is about to say "My boss is a dick" the "dick" is censored by another worker covering his mouth and a jackhammer sound effect.

Rap

In the MTV edit/radio version of Dr. Dre's "Nuthin' but a G Thang", at the line "You know and I know / I'll throw some old funky shit", the "shit" is replaced with Snoop Dogg putting a finger to his lips and says "Shhhhhh!".
In the video for Xzibit's "What U See Is What U Get" Xzibit stops rapping and puts his finger on his lips upon saying the "shit" in "got my own shit loud".
When the OC of Spring Awakening performed at the Tony Awards, they self-censored "Totally Fucked" and "The Bitch of Living" by clapping their hands over their mouths.