Opeth is a must.

Their album Watershed is a masterpiece.
I'll pick out a list of good ones on my computer:
Alestorm - Pirate Metal (it's a fun band more than anything)
Amon Amarth - Viking Metal (it's harder and less folky than other Viking bands)
Anaal Nathrakh - These sound quite extreme, I don't know if they'll be anybody's cup of tea.
Anathema - a very good Doom Metal band - they seem to have a Pink Floyd influence, certainly as they keep covering their songs. Their music can vary a bit.
At the Gates - the fathers of the 'Gothenburg' sound, a Swedish melodic kind of death metal - it's because of these we get bands like In Flames
Behemoth - Polish blackened death metal band.
Black Label Society - I should hope you already know of these - the frontman, Zack Wilde has played for Ozzy Osbourne.
Blind Guardian - power and folk metal
Chimaira - a mainstream metal band
Dimmu Borgir - Norwegian melodic black metal band (one of my favourite bands)
Haggard - folk metal, though they've very much focused on the folk, their band is quite large as they don't cheat and use keyboards to get that symphonic sound. They tend to carry a lot of fantasy themes, heck the album 'Tales of Ithiria' has a narrator
The Haunted - a gothenburg band
Iced Earth - power metal, and a top notch band
Kamelot - a gothic band with a very good singer - highly recommended, I went to see them a couple of months ago and wow! They were really good.
Katatonia - a good doom metal band from Sweden
Mayhem - one of the top guys for black metal, and one of those bands that have stories associated with them, some might find them quite sick.
Metallica - of course

I'd say keep away from St Anger and earlier albums are better.
Nevermore - the guys are really good (currently listening)
Nightwish - a high recommendation, they're an operatic sort of metal, the lead singer (and ex-lead singer) are very good and a real treat to watch live.
One Minute Silence - A Nu metal band from Ireland, very political, though they've split up now.
Paradise Lost
Stratovarius - a power/symphonic metal band, it was their sound that influenced Nightwish
Symphony X - a symphonic metal band, with some quite epic track, Diving Wings of Tragedy is about 20 minutes long.
The Tarjas - Ex-Nightwish vocalist Tarja's band, basically what she decided to do after leaving. Though the album seems to be a moan at Nightwish, it's good to listen to.
Ted Maul - adreneline fueled, as are their mosh pits, their music is quite extreme and they sometimes mix in with a bit of DnB, which works well.