Note: I only chose a few videos that I felt added meaning to the song.
Wake Me Up When September Ends
This video/song can be interpreted in many ways. Wake Me Up When September Ends was said to have been originally written about the death of Billie Joe's father, but the video clip makes obvious references to war, and how devastating it can be. A girl's fiancé enlists in the Army, and the girl is upset and argues with him, as she knows he might not make it out alive. It shows images of soldiers in action, and also of the young fiancé dying. It conveys Green Day's feelings towards war clearly.
Holiday
In this film clip, Green Day are riding in a car through different cities with various backgrounds. Billie Joe is standing on top of the car, surfing, indicating that they are having a great time. In the bar scene, Tré is dressed up as a woman, and it shows him doing cartwheels. It also has everyone drinking and gambling, indicating fun. In the end, it shows the band driving into the desert, where their car breaks down. This "holiday" atmosphere is in contrast to the lyrics which are talking about how George Bush is running the USA like Hitler ruled Nazi Germany ("Sieg Heil").
Warning
The song is about living with endless warnings all around us. We are constantly being told what to do and not to do. The guy in the song is shown ignoring or contravening all the warnings, and the following are examples:
Redundant
In this video clip, it shows the same things happening over and over, ad nauseam. It shows the same girl picking up the same newspaper and reading it, it shows the same guy changing the same painting, the same little girl climbing out the same window, the same woman changing the same painting, the same cowboy walking through the room, etc. With each sentence, a new person appears doing a new thing, but they are replayed over and over. At the end, as the band walk out, Billie Joe picks up the first girl's newspaper, and as she bends over to pick it up, she realises it's not there, and lets out a blood-curdling scream, as it has interrupted her routine.
Basket Case
This video shows the band in a mental asylum. Mike is wheeled in on a stretcher, and Tré is pushed in on a wheelchair. In the beginning, it shows a nurse guiding Mike to his microphone, and helping him put his guitar strap over his head, as he is depressed. It shows Billie Joe in a room by himself, looking like he's slowly going insane. The video shows Tré and Billie Joe 'tripping out' on their prescribed medication, and Mike throwing something through the window, in the hopes of breaking it and being able to escape.
The Saints Are Coming
In this video, which is a collaboration with U2, they show images of what happened to New Orleans after the disastrous Hurricane Katrina, and also show fake news reports on the crisis.
Left: Still from video "The Saints are Coming"; centre: Still from "American Idiot" video; right: still from "Boulevard of Broken Dreams"
American Idiot
In the background of this video, there is a huge white and green US flag erected in the background, and by the end of the video clip, the paint has washed off it, which I assume means that the pieces of America that they care about are fading away.
Boulevard Of Broken Dreams
This song is about Jesus Of Suburbia being alone on the streets, and the video reflects that. It shows the band walking through the desert, as their car has broken down (see Holiday, above), and the effects and pictures in the video add to the feeling of being lonely (such as the tumbleweeds blowing across the sands). The film looks deteriorated, with scratches and marks across it, as if it is "broken" like the dreams of the title.