Can I choose a song from every album? There's too many to choose. xD So glad you made this thread. ;)
The first song that always pops into my head right away is Letterbomb from American Idiot. I'm not sure why I like it so much, I just really do. Christie Road is another one that comes to mind, from Kerplunk. Again, I'm not sure why, I just love it. Minority is another that I love because of the message in it, and it reminds me of what Green Day has taught me during my time as a fan. I'll stop before I get all heartfelt on everyone who doesn't care. xD
And yes, 21st Century Breakdown, their new album, is definitely worth the buy. ;D