I haven’t listened to nearly enough albums, but these are my top 5:
1. Green Day - American Idiot
Favorite album for sure. Boulevard of Broken Dreams and American Idiot got me into Green Day, and Green Day got me into rock music. Every song on this album has its own personality, and every one is great. Jesus of Suburbia and Homecoming are both 9-minute epics, and every minute is worth it. Either could be considered Green Day's best song. Also, the whole album tells as story.
Favorite Song: Holiday. Cool guitar riff, catchy and memorable lyrics, and the megaphone rant is the icing on the cake.
Other Favorites: the rest of the album
2. Alice In Chains - Dirt
AiC's best album. Masterpiece. Enough said.
Favorite Song: Rooster. The song that made me like AiC
Other Favorites: Dam that River, Rain When I Die, Them Bones, Would?
3. Smashing Pumpkins - Mellon Collie and the Infinite Sadness
I love this album. It is very long, crossing the 2-hour mark, but it is so good. There are fast-paced songs like Bullet with Butterfly Wings but they're balanced out by slower pieces like Thirty-Three. And despite its long runtime, there is little filler.
Favorite Song: Zero. Beautiful guitar riff, plus the sound of it memorable and the vocals are great as well.
Other Favorites: Muzzle, Here is No Why, Thirty-Three, 1979, Thru the Eyes of Ruby
4. Red Hot Chili Peppers - Californication
Dreaming of Californication... Very good album, a little all over the place stylistically (compare Easily to Porcelain) but it somehow works.
Favorite Song: Californication
Other Favorites: Parallel Universe, Scar Tissue, Otherside, This Velvet Glove
5. Alkaline Trio - From Here to Infirmary
The most obscure album on here, but it definitely earns its #5 placement. It has some of the best guitar riffs I've ever heard, along with very strong songwriting. The Alkaline Trio is overall a great band that deserves more recognition, and I think this is their best album.
Favorite Song: Private Eye
Other Favorites: Mr. Chainsaw, Stupid Kid, I'm Dying Tomorrow, Trucks and Trains
Honorable Mentions: other albums by the same bands
Green Day - Insomniac
Favorite Song: Geek Stink Breath
Alice in Chains - Alice in Chains
Favorite Song - Heaven Beside You
Smashing Pumpkins - Siamese Dream
Favorite Song: Today; I also enjoy Mayonaise and Cherub Rock
Alkaline Trio - Good Mourning
Favorite Song: Emma