
Megadeth
This is the Dave Mustaine super-band. It took me awhile to really get into Megadeth, but it's pretty rewarding once you do. Megadeth was started shortly after Mustaine was kicked out of Metallica for being an belligerent drunk. Their first release was the album "Killing Is My Business...and Business is Good!", where Mustaine attempted to regain his integrity and "street cred" by showing everyone his awful (and original) version of "The Four Horsemen".
MEGADETH - Countdown To Extinction
Other Albums To Get:
Peace Sells...But Who's Buying
Rust In Peace

ANTHRAX
A great band that didn't take themselves too seriously--they had songs about super-cops and comic books. These guys fucking ripped--every album with Belladonna was gold. Hopefully you caught them on their 2006 reunion tour. If you didn't--you're shit outta luck.
Anthrax - Among the Living
Other Albums to Get:
Fistful of Metal
Spreading the Disease
State of Euphoria
Persistance of Time
The Greater of Two Evils

Metallica
This band is the centerpiece of "thrash metal". They had an awesome 5 album run before devolving into has-beens and trend followers. Who knows though, maybe the new album won't be totally fucking awful.
Metallica - Master of Puppets Part 1 -- Part 2
Other Albums To Get:
Kill 'Em All
Ride The Lightning
...And Justice For All

Slayer
This is one of the few bands of the genre who I actually like, or rather, can tolerate as human beings. Living Legends and not extremely full of themselves. Also one of the few of these bands that I STILL like (in terms of new material).
Slayer - South of Heaven
Other Albums To Get:
Reign in Blood
Seasons in the Abyss
Hell Awaits
Divine Intervention
Show Mercy
(All of Slayer's Discography is fine, the only album I dislike is Diabolus in Musica)

EvilDead
I wrote a post on these guys awhile ago--there's not much to add upon my previous description. These guys popped up in CA sometime in the late 90s when Thrash was out of vogue, but were still pretty fucking good. Unfortunately, they were ignored and dissolved shortly after their second album.
EvilDead - Annihilation of Civilization

Sepultura
Brazilian Thrash. Band got stupid when Max Cavalera left the band. They also got pretty Nu-Metal.
Sepultura - Beneath The Remains
Other Albums To Get:
Schizophrenia
Arise
Chaos A.D.
Roots

S.O.D. and M.O.D.
I hate Billy Milano. S.O.D. features Scott Ian (rhythm guitar), Dan Lilker, and Joey Benante from Anthrax, which adds up to an awesome line-up, and keeps Milano from influencing and tainting the music with too much of his fat-douchebaggery. M.O.D. is Milano's other band, titled M.O.D. because he was too stupid and uncreative to come up with a band name that wasn't ripping off the name of his other band.
S.O.D. - Speak English Or Die
M.O.D. - U.S.A. For M.O.D.

Exodus
This is the band that Kirk Hammett was in before he joined Metallica and replaced Dave Mustaine on lead guitar. Tons of hits on their first album, including Pirahna (PIRAHNAAAAH) and Strike Of the Beast. I don't really care for their albums beyond this one.
Exodus - Bonded By Blood
Beyond Thrash:

Cannibal Corpse - Eaten Back to Life
Cannibal Corpse's Thrashiest (and first!) album. A must have, and one of my favorites

GWAR - Scumdogs of the Universe
A band wrapped in satire that has a pretty interesting musical-scape, from old-school hardcore to thrash.

RAMMER - Cancer
Death meets thrash. This is a relatively new band...but they went and broke up. Great album. Download it. (and buy it!)

System of a Down - Self Titled
First album by a great band I used to listen to a lot in high school.

