I don't know about the best albums of all time, but for my personal favorites: (in no particular order)
Rust in Peace - Megadeth (1991)
You want a good thrash metal album? Look no further. This album locks you in right from the opening riff to Holy Wars... The Punishment Due, and keeps you interested right until the last notes of Rust in Peace... Polaris. This album has all that a good metal album should have: awesome guitar solo tradeoffs between Dave Mustaine and Marty Friedman, kickass basslines by David Ellefson, and insane drums by Nick Menza. Combine that with catchy riffs (every single track on the album has them) and enough diverse material to keep you interested until the very end, and we have what is probably my favorite album of all time. I'll say right now that Dave Mustaine isn't the best singer, and his vocals are hard to get used to if you aren't into Megadeth, but that doesn't matter at all when the rest of the album is this awesome.
Favorite song: Holy Wars... The Punishment Due (although it's a very hard choice)
Follow the Reaper - Children of Bodom (2000)
This is the album that made melodic death metal my favorite subgenre of metal. Music can be both beautiful and brutal at the same time. This album shows it. I can only describe some of the keyboard melodies on this album as being "hauntingly beautiful". And don't get me started on the brutal guitar riffs this album has to offer. This is definitely worth a listen if you're into melodeath, or just metal in general, or just MUSIC in general.
Favorite song: Everytime I Die
Somewhere in Time - Iron Maiden (1986)
I know that everyone who's an Iron Maiden fan is thinking "why THIS album?" Yes, this is the same band that produced The Number of the Beast, Piece of Mind and Powerslave. I enjoy all of those albums, but Somewhere in Time holds the spot for my favorite Maiden album. I find that the keyboards actually go really well with the songs on this album, even though I know that a lot of fans hated them.
Favorite song: Sea of Madness
Death Unlimited - Norther (2004)
My favorite album from another one of my favorite melodeath bands. I love this album not just because of the music, but for the lyrics. I find them to be really powerful (even if I have to look them up to understand them), and I can relate to a lot of them, as someone who's gotten through some really tough moments in life. Unrelated, but I think I'm one of the few people who actually discovered Ensiferum through Norther, and not vice versa.
Favorite song: Nightfall/Deep Inside
Curse of the Red River - Barren Earth (2010)
To most people, this is probably just another great melodeath/progressive metal album. To me, it's so much more. I saw them opening for Finntroll and Ensiferum in 2011, and it was at that show that I met a really nice guy. We hit it off immediately, and he offered to buy me a drink and wanted my phone number. After the show, I walk out with him to the merch stands and decide to buy this CD, since I really liked the band. It was then that I actually met the band, and they were really nice and signed my CD. Unfortunately, I lost track of the guy I met, and we never saw each other again. Listening to this CD always reminds me of that magical night I had. And who knows? Maybe it's better this way, since I don't have any negative opinions of him.
Favorite song: Our Twilight
Holographic Universe - Scar Symmetry (2008)
Christian Älvestam is the most talented metal musician out there today. It's rare that I word a sentence that is just my opinion that way, but this guy not only has an outstanding guttural range, he has an amazing range with his clean vocals, too. The vocal harmonies on this album are outstanding. With most songs I like, it takes several listens to really love the song. I loved most of these songs the first time I listened to them.
Favorite song: Morphogenesis
Ride the Lightning - Metallica (1984)
This is it. This is the album that got me into metal. I've always liked metal, but this album made me a die-hard metalhead. And yes, I like this album better than Master of Puppets. I think that the reason is probably that I think MoP has both brutal riffs and good melodies, but it never really combines the two. This album is brutal and beautiful at the same time.
Favorite song: I literally can't choose one. Metallica is the one band that I've never been able to pick a favorite song of. I'd probably choose either Ride the Lightning, Fade to Black, Trapped Under Ice or Creeping Death, and that's already half the album.
Fiction - Dark Tranquillity (2007)
Dark Tranquillity is one of the few bands I will admit to being a bigger fan of their later material. I really think that in the 2000s, they really began to establish their own unique sound. Yes, this is a metal album, but it's also.. calming. I absolutely love the piano in this album.
Favorite song: Icipher
Natural Born Chaos - Soilwork (2002)
I'm being quite redundant in my descriptions, but this is another "brutal and beautiful" album that I love. I love listening to this when I'm driving. As someone who lives just over 30 miles from school, I drive a lot, and this is often the album I choose to listen to.
Favorite song: this is another album I can't chose a favorite song from.
Twilight of the Thunder God - Amon Amarth (2008)
If there's any band that makes you feel like a viking, it's Amon Amarth. And this is undoubtedly their best work. (yes, another band who got better as they aged, although I think most people agree with me in this case) When I listen to this album, I'm not driving a 2009 Hyundai Elantra, I'm driving a viking longboat. I'm not in boring SoCal, I'm plundering villages in Norway. And I'm able to grow a full beard despite being a woman. Does it makes sense? No, but it doesn't have to when you're listening to something as kickass as this.
Favorite song: Live for the Kill
Of course, I have a lot of favorite albums, so these are subject to change. Some albums I wanted to add to the list but ran out of room for:
Painkiller - Judas Priest
The Jester Race - In Flames
Fragments of D-Generation - Disarmonia Mundi
Killing Is My Business... And Business Is Good - Megadeth
Kill Em All - Metallica
Seasons in the Abyss - Slayer
Screaming for Vengeance - Judas Priest
And of course, I tried to avoid albums by the same bands.