If you like a little electronics in your music, I'm really hooked on Matt & Kim right now. Their new album Sidewalks is killer as is their last album Grand.

Also, If you do not own The Flaming Lips album Soft Bulletin, you are missing out on life.

Nah, I think it's safe to skip The Suburbs. 

I've been getting into prog rock lately. Some albums I can definitely recommend include 2112, Moving Pictures and everything released in between by Rush, Thick as a Brick and A Passion Play by Jethro Tull, and Foxtrot by Genesis (yes, there was once a time before I was born when Genesis was cool. Who knew?). If you want to hear the roots of prog, check out King Crimson's Court of the Crimson King. Pink Floyd was already mentioned, but I think Animals is a better album than Dark Side of the Moon.

For something more modern, try any album by Metric, Welcome to the Night Sky and New Inheritors by Wintersleep, and Them Crooked Vultures.

Queen's Greatest hits 1 & 2, I prefer Division Bell from Pink Floyd and I would also recommand some Radiohead albums like OK Computer and The Bends.

...And Justice For All

Edit: Acualy all 80s Metallica

Figure Number 5 by Soilwork!

Anything by Bloc Party

Decemberists - Hazards of Love

All great suggestions. I'd like to add something.For Rush, I'd recommend to listen to live albums like R30, Snake & Arrows Live, Rush in Rio, Different Stages, etc., etc, live perfomarnce it's very different from studio performance.   For, Pink Floyd, I'd say you shouldn't miss Wish You Were Here (probably my favourite album ever). Talking about the roots of prog I'd suggest Aphrodite's Child 666 (1972). If you want something more modern I'd suggest Dream Theater (only the albums from the 90s, because now they suck), it's Metal/prog, albums like Images And Words, Awake and Metropolis Pt.2. I also like Porcupine Tree, search for: Fear Of a Black Planet, In Absentia, Arriving Somewere (live)

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If you want some more conventional pop/rock, my pick is Elton John. Even if he is a very famous artist, I think not many know very much about his music nowadays. I think he is really a great musician, still to really appreciate him you should listen to it's live albums, it's about 10 times better than studio. In particular I suggest Live In Australia (with the Melbourne symphony orchestra), Live  in Barcellona (with the band) and Live in Ephesus (a solo piano performance). To stay in pop/rock of course Queen are great and I also like very much Sting and The Police: check for Certifiable live.

During High School years I've been into Metal and stuff very much, excpecially into Heavy Metal and Hard Rock. If you like that genre I'd suggest you to listen to Iron Maiden: Live After Death and Rock In Rio; Rainbow: first albums; Judas Priest: Unleashed In the East, British Steel, Painkiller; Saxon: first 3 albums. If you prefer something more on the trash/death side I like Slayer and Kreator (check for live albums) and Testament: Fist Strike Still Deadly, The Gathering. I generally don't like black metal but Arcturus are an exception, check for:  La Masuqerade infernale, The Sham Mirrors. I also like a lot Nevermore: Dead Heart In A Dead World, Enemies Of Reality, This Godless Endeavour. I could add more there but it's getting long....

Lately I'm starting to geta bit into funk, I've got 2 albums from The New Mastersounds I like very much: Ten Years On, 102%. I'm also stantring to listen to Tower Of Power but I can't suggest any particual album atm.

At last, I'm also into the work of Vangelis, a composer who started as a prog/rock musician (he composed the 666 album mentioned before), then he became a pioneer in electronic music, he composed studio albums like Heaven And Hell, China, and also composed movie and documentary scores like Opera Sauvage, Blade Runner OST, 1942: Comquest Of Paradise OST. Another movie score composer I like a lot is Enio Morricone.

Well I put a lot of different albums and genres, I hope you find something you like.

Some of my personal favorites that you may enjoy are...
› The Smashing Pumpkins ~ Siamese Dream
› The Kinks ~ Muswell Hillbillies
› Blue Oyster Cult ~ Fire of Unknown Origin
› Zwan ~ Mary Star of the Sea
› Lou Reed ~ Transformer
› Led Zeppelin ~ Physical Grafitti
› The Clash ~ Give "Em Enough Rope
› The Beatles ~ Rubber Soul
› Blue Cheer ~ Outsideinside
› Professor Longhair ~ Crawfish Fiesta

Anything done by the White Stripes/Raconteurs
The House that Dirt Built - The Heavy
Everything by the Red Hot Chili Peppers (not an option)
Everything by Radiohead
Oh No - Ok Go
Ready for the Weekend - Calvin Harris (not really rock, but I figured I'd throw some other stuff in)

U2 - All that you can't leave behind