Metallica has been my intro to heavy metal. (BTW, Load and Reload is painfully underrated, and St. Anger had some good ideas, but was way too unpolished). I also like some of Dream Theater's stuff, Porcupine Tree and Anthrax. Good stuff.
Metallica was my introduction to real Heavy Metal, and used to be my favourite Metal Band. That position has since been taken by Avenged Sevenfold, though, since the release of Nightmare (The Rev is my favourite drummer ever, and the fact that they dedicated an entire album to his memory is simply fantastic!)
Other Metal Bands I really enjoy are
-System of a Down
-And many many more!
I love lots of other bands, though. I have a soft spot for Iron Maiden, as they got me into metal. Seventh Son of a Seventh Son is my favorite of their albums.
Dream Theater is another favorite. Again, I prefer their earlier (pre Six Degrees of Inner Turbulence) albums, but their latest, A Dramatic Turn of Events, might be their best since their concept album, Metropolis pt. 2: Scenes from a Memory.
Finally, there's Savatage, whose output is so diverse that it's hard to believe they're the same band by the late 90s that they were in the early 80s. Highlights are The Dungeons are Calling, Hall of the Mountain King, Streets: A Rock Opera, Edge of Thorns, Dead Winter Dead, and The Wake of Magellan. That's what, half their output? Yeah. Fantastic band.
Other great bands are Theocracy, Sonata Arctica, Blind Guardian, Galneryus, Kamelot, Candlemass, Cathedral, Trouble, Nightwish, Metallica (pre Black Album), Opeth, Ayreon, and Avantasia. I'm sure several are missing from my lsit.
Bullet For My Valentine
Thousand Foot Krutch
War of Ages
Day To Remember
The Letter Black
Three Days Grace
I guess since they asked for one, I'll provide one. Bullet for My Valentine. I am, like, obsessed with these guys. Now, actually, they're probably more borderline between metal and hard rock, but they've been my "favorite band" (term used loosely) for the last three-ish years. I literally listen to them all day in some instances. They are insanely talented, and I don't think I really have heard a song performed by them that I didn't like. Have to say my favorite album of theirs is Scream Aim Fire, my favorite track being Take It Out On Me.
A little while ago, because my dad has been a fan of a lot epic metal bands for, like, ever, I tried to get him into Bullet. And he was reluctant because he doesn't really care for the "screaming"... but, he finally gave in, and now he keeps talking about them and calling them a really "tight band" and I feel so successful now. xD I knew he would like them because the bands he likes are some of the bands that inspired BFMV's music style, so yeah.