Punk bands, rock bands and punk rock bands:
Below are some of my favorite bands, I know not all of them are punk rock, but If you like Green Day odds are you'll like them. They're in alphebetical order to make it easy to find a band.
Blink 182- Rockin tracks you've gotta hear: Adam's song(Enema of the state), Go (Blink 182)

Find out more?: www.blink182.com
Everclear- Rockin songs: Sparkle (World Of Noise), Unemployed Boyfriend (Songs From an American Movie Part 1), Rock Star (Songs from and American Movie part 2)

Find out more?: http://www.vh1.com/artists/az/everclear/artist.jhtml
Fallout Boy- Rockin' songs: Sugar we're going down, dance dance, A little less sixteen candles a little more "touch me", Grand theft autumn.
Find out more?: http://www6.falloutboyrock.com/falloutboy/home.php
Good Charlotte- Rockin songs- Waldolf Worldwide (Good Charlotte) Hold on (Young and the hopeless) In the world (Murder)(TCOLAD)

Find out more?: www.goodcharlotte.com
Green Day (Gods of punk)- Rockin Songs: There's tons I wanna suggest, but I'll tell you some you can hear easily and that'll be good for listening to them for the first time
Basket Case (Dookie, INS) Longview (Dookie, INS) Hitchin' a ride (Nimrod, INS)

Find out more?: All over this site!
Incubus- Rockin songs (I only have one album so there all from Make yourself) Pardon Me, Make yourself and When it comes.

Find out more?: http://www.enjoyincubus.com/
My Chemical Romance- I've only got into this band in the last few months (just before they started to get big) Rockin songs- I never told you what I do for a living (TCFSR) Headfirst for halos (IBYMBUGMYL)

Find out more?: http://www.mychemicalromance.com/
The offspring- Rockin Songs: Pretty Fly (For a white guy) (Greatest Hits) Want you bad (Greatest hits)

Find out more?: http://www.offspring.com/
Sum 41- Rockin Songs: In too deep, Heart attack, Never wake up (all from All Killer, No Filler)

(I thought the pic of them in the phonebox was pretty cool)
Find out more?:http://www.islandrecords.com/sum41/site/home.las
Tenacious D- Rockin Songs: Tribute and Wonderboy (Tenatious D) Yes I know have the abum, and I'n still working through it, if you get it don't play it infront of your parents! Just a warning cause I don't think songs like F*ck her gently are gonna go down too well!)

Find out more?: http://www.tenaciousd.com/
Ramones- Rockin' songs: Blitzkreig bop, The kkk took my baby away, Howling at the moon
Find out more?: http://www.ramones.com