As promised, here's more personal favourites from YouTube. I decided to lump 1970s and 1980s together, so this is a mixed bag, to say the least. 70s has been called the decade taste forgot and 80s was an age of blatant yuppie overkill. All in all, an era of bad haircuts, anyway.
Gladly there's more to this period of circa 20 years than just platform shoes and mullets. This was after all when music video emerged as an independent artform, so alongside my own musical favourites, I've also tried to include some videos that historians consider exemplary milestones in the evolution of this format. (Check A Guide to 1980s Music Video Directors if you want to do more searches on your own.) Thanks to Mr. Jani Hellén for some extra tips.
(And I've made some additions to the 1960s entries -- you might like to check out.)
Also, I'll keep updating this list, so keep hitting that "Reload" button!
ABBA. I guess these days it's OK to say you like Abba, but there's still a silliness factor in their external outlook.
ABC: 'Look of Love'
Adam and the Ants were at the forefront of the early 80s "New Romantic" style.
Baltimora: 'Tarzan Boy'. Authentic Italo trash from the 80s!
Afrika Bambaataa: Planet Rock
'Sounds Like Melody'
Amon Düul II
Art of Noise
The Au-Pairs: 'Come Again'
Tony Basil: 'Mickey'
The B-52's: 'Rock Lobster'
Johnny Rotten of Sex Pistols called Billy Idol the "Perry Como of punk", so this vocalist of the band Generation X who made it big with his solo career in America may not have been the most "street credible" names to emerge out of punk, but I was a big fan of his early-to-mid-80s Rebel Yell/Vital Idol era, and the guy was definitely one of the 80s pop icons like Madonna.
'Eyes Without a Face'
'Dancing With Myself' (a video directed by Tobe "Texas Chainsaw Massacre" Hooper, with a glimpse of Octobriana too!)
Blancmange: 'Blind Vision'
Bootsy's Rubber Band: DC live, 1978
David Bowie ruled the 1970s almost single-handedly. As far as my own memories go, his 'Ashes To Ashes' (1981) was for me the first example representing the new style of music video art (looking quite strange and scary for a young kid). It's too bad music video declined pretty quickly as a bona fide artform, and became (in most cases) just glossy and shallow promotion for hit singles (just witness any bling-bling R&B videos on today's MTV).
Sarah Brightman: 'I Lost My Heart to a Starship Trooper' (feat. Hot Gossip. The appearance of Hot Gossip dance troupe (familiar from Kenny Everett Show) is what makes this one interesting.
Bronski Beat: 'Smalltown Boy'
'I Am A Camera'
'Video Killed The Radio Star': the first-ever video shown on MTV, on the 1st of August, 1981!
Cameo: 'Word Up' (1986)
Can: 'Paperhouse' (live on Beat Club)
'Meet You In The Subway' 
Classix Nouveaux: 'It's A Dream'
Julian Cope: Trampoline
The Cult: 'She Sells Sanctuary' (1985). The guilty pleasures dept...! The Cult was a band that started as a gothrock band called Southern Death Cult, then had a total makeover to pompous 60s/70s retro-style (stadium) rock. A must for the fans of unintentional humour, but I still think there's something endearing in their pseudo-mystical, quasi-psychedelic mid-80s stuff.
The Cure, who had some classic music videos in the 80s.
DAF: Liebe auf den ersten Blick'
The Damned: 'New Rose'
Danielle Dax: 'Big Hollow Man' (1988)
Hazell Dean. UK Hi-NRG disco...
Dire Straits: 'Money For Nothing'. Not my own favourite bands, but this 1985 video with its now amusing-looking early computer animation is considered a classic.
Devo: those magnificent men in their red flowerpot hats...
Dinosaur Jr.: 'Freak Scene'
'I'm So Beautiful'
Dominatrix: 'The Dominatrix Sleeps Tonight'. A cult dance hit from 1984. This video was banned on MTV.
'The Chauffeur' (their infamous black & white video with girls in lingerie, somehow reminiscing Helmut Newton -- and a great song!)
Echo & The Bunnymen: 'People Are Strange'
Einstürzende Neubauten: 'Sand'
Roky Erickson, the legendary madcap front man of the 13th Floor Elevators.
Fad Gadget: 'Collapsing New People'
'Rock Me Amadeus'
'Cab It Up'
live on The Tube (1983)
Frankie Goes To Hollywood
Funkadelic / Parliament
Peter Gabriel: 'Sledgehammer'. A classic music video with stop-motion animation.
Gloria Gaynor: 'I Will Survive'
Herbie Hancock: 'Rockit' (1983). Classic electro track and a classic video! + 'Rockit' - live at Grammy Awards 1984
'Don't Waste My Time'
'19'. This mid-80s UK hit about the Vietnam War introduced the technique of sampling to the audience at large.
'Let Me Go'
'This Is Mine'
especially their pioneering 'Being Boiled' from 1978.
Iggy Pop / The Stooges
Michael Jackson: 'Thriller'. I'm not a Jacko fan myself, but this 13:33 clip (or rather, a short film) is certainly a milestone in music video history. "Due to my strong personal convictions, I wish to stress that this film in no way endorses a belief in the occult", he points out in its beginning.
The Jam: 'Going Underground'
'Cantonese Boy' (on Old Grey Whistle Test)
'Gentlemen Take Polaroids'
'Ghosts' (on Old Grey Whistle Test)
'Visions of China'
Grace Jones: some awesome classic music videos!
Howard Jones. Another 80s synthpop star who seems to have been forgotten now.
Kajagoogoo: 'Too Shy' (1983)
'Einstein a Go-Go'. They gave the name to a "New Romantic" disco in Helsinki!
Liaisons Dangereuses: 'Los Niños Del Parque'
Malaria!: 'Geld - Money'
'Madame Butterfly (Un bel di vedremo)'. Opera meets disco.
My Life With The Thrill Kill Kult: 'Kooler Than Jesus'
Mötley Crüe. Yes, more guilty pleasures...
Newcleus: 'Jam On It'. A New York electro classic from the early 80s.
New York Dolls
Nine Inch Nails: 'Head Like A Hole' (1989)
The Normal: 'TV OD' (1978). The Normal was the electronic one-man project of Daniel Miller who founded Mute record label.
Philip Oakey: 'Together In Electric Dreams'
Robert Palmer: 'Addicted To Love'. Robert Palmer and his "band" of supermodels.
Pet Shop Boys
'Another Brick In The Wall'
'Any Colour You Like'
'Careful With That Axe, Eugene'
'Empty Spaces/What Shall We Do Now?' (animation from The Wall movie)
Live at Pompeii
Plastic Bertrand: 'Ca Plane Pour Moi'
I am a huge fan of Prince's "Golden Age" (ca. 1979-88) music; a big early influence on me and my musical education, which was to open up for me whole worlds of rock, pop, soul, funk and psychedelia. Here was an artist who was a combination of Jimi Hendrix, James Brown, Sly Stone, Curtis Mayfield, et al., and also played all instruments on many of his records and produced it all himself. It's a pity he couldn't keep up the promise of those days. Here are some videos and live performances from that era:
'Darling Nikki' (live, early 90s)
'If I Was Your Girlfriend'
'I Wanna Be Your Lover' (on American Bandstand, 1980)
'I Wish U Heaven'
'Let's Go Crazy
'Little Red Corvette'
'Party Up': "You gonna have to fight your own damn war 'cos we ain't gonna fight no more!"
'Purple Rain' (film version)
'Purple Rain' (on American Music Awards, 1985)
'When Doves Cry'
'Why You Wanna Treat Me So Bad' (on American Bandstand, 1980)
Live in 1983:
    
VJ Jazz vs Prince A-U-T-O-Matic Edit. A video megamix!
(See also some Prince collaborators such as Sheila E, Morris Day & The Time, Vanity 6 & Apollonia 6 (girl groups which Prince dressed up in lingerie). Sinead O'Connor's 'Nothing Compares 2 U' was originally penned by Prince.)
Public Enemy: my all-time favourite hip-hop act.
Public Image Limited / PiL
(see also: Snakefinger: 'The Man In the Dark Sedan')
Queen -- I know there are some people who hate this band with a passion but some consider their 'Bohemian Rhapsody' (1976) one of the first modern-style music videos.
Ryuichi Sakamoto + Kiyoshiro Imawano: 'IKENAI Rouge Magic' (1982)
'122 Hours of Fear'
Sid Vicious: 'My Way'
Sigue Sigue Sputnik:
'Love Missile F1-11' (1986). SSS were basically a "cyberpunk meets glamrock" one-hit wonder who kept repeating the same simplistic song formula throughout their career, but I loved them as a sort of proto-techno, and especially their ultra-pop visual side, well represented on this video; referencing the sci-fi fantasies of Blade Runner, Clockwork Orange and Mad Max films with sex, (ultra-)violence and war.
Silicon Teens: 'Memphis Tennessee'
Siouxsie and the Banshees
The Sisters of Mercy
'The Choke' (live 1987)
'Worlock' (the original banned video from 1989)
Patti Smith: 'Gloria'
'Sex Dwarf' (the banned version) (sorry, bad image quality)
Coil's version of 'Tainted Love')
Jimmy Somerville & Marc Almond: 'I Feel Love'/'Johnny Remember Me'
Sonic Youth with Lydia Lunch: 'Death Valley '69'
SPK: 'Metal Dance'. Industrial from 1984.
Bruce Springsteen. It may come as a surprise to some people that I'm a bit of a Springsteen fan (though my own knowledge of his albums ends somewhere in the mid-80s), but what appeals to me in his songs is the way he tells stories there.
Suicide: 'Ghost Rider'. The seminal electronic duo of Alan Vega and Martin Rev.
Tears For Fears
Throbbing Gristle: 'Discipline'. The real pioneers of industrial. See also: Psychic TV.
The Timelords: 'Doctorin' The Tardis'. A project of The KLF combining Dr Who theme to Gary Glitter's Rock'n'Roll.
Toyah. She may be forgotten now but the minuscule Toyah Willcox was one of the biggest stars of the late 70s/early 80s "New Romantic" UK scene.
Van Der Graaf Generator
I think with this "New Romantic" synthpop band headed by the costumeplay-loving Steve Strange there was a lot of "image over content", but they were combined together of some of the finest new wave era musicians such as Midge Ure and John McGeogh, so musically there were many memorable moments, 'Fade To Grey' perhaps the biggest classic of those. And this band was just made for music videos.
'The Damned Don't Cry'
'Fade To Grey': their finest moment from 1981, and my all-time favourite in the whole synthpop genre.
'Mind of a Toy'
Scott Walker: 'Track 3'. "After a brief 'The Sun Ain't Gonna Shine Any More" retro clip, Scott is subjected to a painfully brainless Scottish VJ's inane questions. Then, the "Lynchian" video for 'Track 3' off Climate of Hunter."
W.A.S.P. (yes, every little boy must go through a heavy metal period!):
'Animal (F**k Like A Beast)'
'I Wanna Be Somebody'
We've Got A Fuzzbox and We're Going To Use It: 'Love Is The Slug'. 80s girl power!
Yazoo. A short-lived synthpop duo of Vince (Depeche Mode/Erasure) Clarke and Alison Moyet.
Yellow Magic Orchestra / YMO
Zolar X. A glam rock era "house band" at Rodney Bingenheimer's English Disco in LA, who were dressed as aliens.
Films and TV:
(As you can see, I'm especially a fan of bad retro sci-fi...)
The Adventures of Buckaroo Banzai Across The 8th Dimension (1984)
All In The Family: opening credits. This TV comedy about a conservative redneck Archie Bunker having to face more liberal times of the post-hippie era was a big hit in the 70s.
Apple Computers: a Ridley Scott-directed commercial from 1984.
Atari 80s TV commercial + Yar's Revenge + Atari Turmoil + Atari E.T. Christmas Ad (1982)
BBC Hip Hop Documentary (1984)
Beat Street: battle scene from the hip-hop movie.
The Bird With the Crystal Plumage by Dario Argento: trailer.
Blade Runner +
"Director's Cut" trailer + Roy Batty
Brazil (1985) by Terry Gilliam: trailer.
The Brood (1979) by David Cronenberg: trailer.
Buck Rogers: the TV series opening credits
Cannibal Holocaust: opening scene + more
Coca Cola ad of the Hilltop Campaign: (1971) "I'd Like to Buy the World a Coke". A TV commercial.
Commodore 64 - More computer for less money. A TV commercial from the 80s.
Die Hard (1988) by John McTiernan: trailer.
The Equalizer. Opening credits to the 80s TV series starring Edward Woodward. Great title music too!
Fast Times At Ridgemont High (1983): trailer.
Flashdance (1983): dance intro.
Flash Gordon (1980): trailer
Exorcist. William Friedkin's 1973 horror flick which spawned a series of inferior sequels.
Fantastic Planet (1973) Rene Laloux's bizarre animation film adaptation of Stefan Wul's allegorical science-fiction novel, here in its entirety.
Bill Gates: "Macs are cool" (1983)
The Godfather: opening titles
"I Want My MTV!": an 80s commercial with Billy Idol, Cindy Lauper, David Bowie and Boy George.
Jaws: the trailer.
Juicy Fruit commercial from the 80s.
Knight Rider: opening credits. David Hasselhoff and his talking car: aargh...!
Liquid Sky: a short clip from the 1982 cult film by Slava Tsukerman.
Little House on the Prairie opening credits: OK, I confess -- I used to watch this when I was a kid.
Maniac (1980): trailer for a slasher film.
McDonald's training film, 1972
Miami Vice: opening credits + 'In The Air Tonight' pilot scene + more
Milk, It Does a Body Good. A TV commercial from the 80s.
Monty Python & Monty Python's Flying Circus. "Nobody expects the Spanish Inquisition!" Masters of absurdist comedy.
Phenomena by Dario Argento: trailer.
RCA Selectavision Videodisc Player (1983).
Robocop (1988): trailer.
Return of the Jedi (1983): trailer.
Scarface - the finale scene: "Say hello to my little friend!"
First season opening credits, Eagle crash, Explosion from 'Breakaway' and Second season opening credits.
Spiderman Toei: introduction to Japanese Spiderman show, 1978!
Starsky & Hutch: a beach buggy chase.
The Terminator: trailer.
THX 1138: a mash-up of George Lucas's early dystopian sci-fi film with Björk's music!
Two Evil Eyes by Dario Argento & George Romero: trailer.
UFO (1970): opening credits. Gerry Anderson's first live-action TV series he made before Space: 1999. Gotta love those purple wigs!
Vincent: Tim Burton's dark animated short-film from 1982 narrated by Vincent Price.
more 1970s/80s TV show credentials
more 1980s movie trailers
more 1980s TV commercials
Coming up next: 1990s to the present...