Research into the generally named 'Greatest' album covers shows examples of wide rangers of different artists including The Beatles, David Bowie, The Sex Pistols and Nirvana.
Main examples that were typically near the top of almost all lists were;

Arctic Monkeys 

The following videos are what were found on most top music video sites. I have selected the ones I believe are the best ones from those websites.

Michael Jackson's 'Thriller' 



This video is considered one of the best music videos of its time and is still very popular today. During the time of its release, there were no other videos like it as it was one of the very first to exceed the usual length of a music video - it didn't follow stereotypical conventions and can be considered to be a 'short film' as it contains dialogue and lasts for over 13 minutes, which is one of the many reasons why it was so popular. 

a-Ha's 'Take On Me' 



The style of this music was very different during the time of its release as it was set in a half reality/half cartoon style that they merged together, which had never been done before. It was notable for using the combination of pencil-sketch animation and live action called rotoscoping (whereby real footage is traced over) which kept people entertained, and still does even now. 

Nine Inch Nails' 'Closer' 



Although very explicit, this was possibly the most popular of Nine Inch Nails' music videos as it was different and the lyrics, again very explicit, were able to keep people listening. It introduced a new type of music video as it is one of the first to show S&M without censoring. 

Weezer's 'Buddy Holly'



'One of the most creative music videos of the ’90s, Spike Jonze’s take on Weezer’s “Buddy Holly” transports Rivers Cuomo & co. onto an episode of the 1970s sitcom Happy Days. The band plays a show at (where else?) Arnold’s for Richie, the Fonz and the rest of the gang. Jonze’s seamless integration of scenes from the original show with stunt doubles (especially during Fonzie’s dance at the end) as well as the video’s snarky jokes (there’s a “To Be Continued” fake commercial break in the middle of the song) made it one of the most popular videos of the decade. It also cemented Weezer as the era’s geekiest, smartest band.' - TIME

Music video regulations were never considered strict as it has always been possible for people of all ages to watch any video they pleased, even if the video was not recommended for people of younger ages. Until recently, only videos considered to have 'extreme' visuals in them were forced to have regulations placed upon them. 
This year (2014) the BBFC have offered to put new regulations on music videos. 

Government has also asked the BBFC and the BPI to launch a pilot scheme to rate online music videos. At the moment online content does not come under the BBFC’s remit, and so anything sent to it for classification is done so voluntarily (which some labels do in some cases).
Originally, Ofcom was said to put regulations on music videos but they were not effective enough as people can still access all types and age rated music videos online as there is no restrictions online to stop them doing this.