Presented in alphabetical order, because with this many tracks it's impossible to rank them.
1.
Juanes -
A Dios Le Pido
If you're a Spanish teacher, this song is great for teaching the subjunctive. It's also Juanes' best song.
2.
Kaki King -
Air And Kilometers
Kaki King manages to wring an incredible amount of emotion out of her guitar. The breakdown about a minute in is great.
3.
LCD Soundsystem -
All My Friends
Surprisingly, the repetition of the keyboard line for 7 minutes doesn't get tiring, but just adds to the melancholic punch of the lyrics: "You spent the first five years trying to get with the plan, and the next five years trying to be with your friends again."
4.
Yeasayer -
Ambling Alp
It's got a great hook and appealing vocals, but it's the complexity of this song that brings it up a notch: the intricate bassline, the synth run at the end, the drums that anchor the rhythm.
5.
Thom Yorke -
Analyse
Deceptively simple and terribly affecting.
6.
Porcupine Tree -
Anesthetize
Porcupine Tree's best song. Really, each of its three sections could be a separate song and they'd all be great.
7.
Broken Social Scene -
Anthems for a Seventeen Year-Old Girl
Emily Haines' vocals steal the scene, and I didn't really notice how great the instrumentals are until I listened to the instrumental version of this song,
Pitter Patter Goes My Heart.
8.
Regina Spektor -
Après Moi
Sadly, I think this is the only track where Regina Spektor sings in Russian. She should do it more often.
9.
Islands -
The Arm
I'm in the minority in preferring
Arm's Way to
Return to the Sea. The entire album is deliciously complex and unrelentingly intense, and this is its best track. The violins are especially good.
10.
Battles -
Atlas
If this list were ordered, this song would definitely be in the top 5. Battles are one of the most precise and technically skilled math rock bands around, but what sets them apart is their sense of whimsy, which is never more apparent than on this track, which is probably the most fun song of the decade.
11.
Do Make Say Think -
Auberge le Mouton Noir
As a genre, post-rock is often labelled as being formulaic and repetitive, but the compositional complexity of this song shows that creative post-rock is still being produced. The bit starting at 3:30ish is wonderful.
12.
Late of the Pier -
The Bears Are Coming
Another song with a great sense of fun. The combination of an infectious beat with a dance-punk aesthetic is what makes this song.
13.
Crystal Castles -
Black Panther
When you listen to Crystal Castles' debut album, you start to think that you've heard these songs before. The melodies are so basic, so inevitable, that it's hard to believe that nobody's come up with them before.
14.
The Fiery Furnaces -
Blueberry Boat
Yes, this song is about a blueberry boat being attacked by pirates. The "doom chords" (if you know this song, you probably know what I'm talking about) are sheer awesomeness.
15.
Kyte -
Boundaries
I'm surprised at how little attention these guys get. Their debut album was a completely original sound, and this song is complete bliss.
16.
Pure Reason Revolution -
The Bright Ambassadors of Morning
The last four minutes of this song are one of the most epic things you'll ever hear.
17.
Panda Bear -
Bros
For a 12-minute song built around one chord, this is pretty damn awesome.
18.
Animal Collective -
Brother Sport
This is my most listened-to song ever, according to iTunes. It deserves the spot, too.
19.
Pure Reason Revolution -
Bullitts Dominæ
Yet another PRR song.
The Dark Third was one of the best debuts of the last few years, despite the nonsensicality of the lyrics ("And as I ask them inside everlasting the inosphere's collided, everyone's falling, sun-suicide's optimal").
20.
This Will Destroy You -
Burial on the Presidio Banks
This song destroys me. One of the most explosive climaxes in post-rock.
21.
Wolf Parade -
California Dreamer
The best chorus Wolf Parade has ever written, probably.
22.
Vampire Weekend -
Campus
This song is so light and breezy, and any song with the line "spilled kefir on your keffiyah" is good in my books.
23.
Sufjan Stevens -
Casimir Pulaski Day
The saddest song written about cancer before The Antlers released
Hospice.
24.
Muse -
Citizen Erased
I always have a hard time choosing my favourite Muse song, but this song has their best riff (and they're a very much riff-based band) and their best solo.
25.
Porcupine Tree -
Collapse the Light Into Earth
The piano is kind of reminiscent of Coldplay's "The Scientist," but this song is much more affecting. It'd be a good song to play at your funeral.
26.
Joanna Newsom -
Colleen
I can't help but break out into a grin whenever she does the "yip" between verses.
27.
Metric -
Combat Baby
On their tour this year, Metric ended their concerts with a sing-along acoustic rendition of this song. That it actually worked testifies to their melodic genius.
28.
Sufjan Stevens -
Come on! Feel the Illinoise!
I could put this song on the list just for the title.
29.
Mew -
Comforting Sounds
That's funny, I didn't know Mew was a post-rock band. Listen to this song on full volume and you'll be blown away.
30.
Joanna Newsom -
Cosmia
This is the shortest track on
Ys, but it still has more depth than 90% of the songs out there.
31.
José González -
Cycling Trivialities
Simple but beautiful. It's 8 minutes long but it feels more like 3.
32.
Justice -
D.A.N.C.E.
The fact that this is the only dance song that made the list says something about how great it is.
33.
The Mars Volta -
Day of the Baphomets
The section that starts with "I am the reason for your missing child" is so intense. Actually, this entire song is intense.
34.
Wolf Parade -
Dear Sons and Daughters of Hungry Ghosts
Spencer Krug can basically do no wrong, but nowhere is his songwriting stronger than on
Apologies to the Queen Mary.
35.
Under Byen -
Den Her Sang Handler Om At Få Det Bedste Ud Af Det
This is possibly the most underappreciated song ever. It used to be my favourite song, and it's still in my top 5. The climax and piano coda are incredible.
36.
65daysofstatic -
The Distant & Mechanised Glow of Eastern European Dance Parties
Frankly, I don't see how anyone could dislike this song.
37.
Do Make Say Think -
do
Like "Auberge Le Mouton Noir," a beautifully complex post-rock song. It's hard to decide which one is their best.
38.
Architecture in Helsinki -
Do The Whirlwind
Such unadulterated joy.
39.
Yeah Yeah Yeahs -
Down Boy
I used to think that nobody could top Jim Morrison when it comes to yelps, but Karen O certainly comes close in this song.
40.
Sunset Rubdown -
Dragon's Lair
This is Spencer Krug's best post-Apologies to the Queen Mary song, especially the guitars at the end.
41.
Patrick Watson -
Drifters
The delicate piano intro and the wall-of-sound climax couldn't be more different, but they fit together seamlessly.
42.
65daysofstatic -
Drove Through Ghosts to Get Here
Usually when I'm walking and listening to music, I involuntarily step to the tempo of the music. If I did that for this song, I'd be running by the end.
43.
Joanna Newsom -
Emily
This song contains Newsom's worst lyrics ("peonies nod in the breeze and while they wetly bow with hydrocephalitic listlessness, ants mop up their brow"), but also some of her best ("I dreamed you were skipping little stones across the surface of the water, frowning at the angle where they were lost and slipped under forever, in a mud-cloud, mica-spangled, like the sky'd been breathing on a mirror" and "the ties that bind, they are barbed and spined and hold us close forever"). I could go on about this song, but I won't.
44.
At the Drive-In -
Enfilade
The amount of energy in this song is remarkable.
45.
Cloud Cult -
Everybody Here Is a Cloud
Making lyrics about mortality fun!
46.
Radiohead -
Everything In Its Right Place
This is a rarity, a song that grabs you from the very first note, and keeps your attention until the end.
47.
The National -
Fake Empire
There's an entire group on last.fm dedicated to this song, and not without reason.
48.
Andrew Bird -
Fake Palindromes
This is one of the few tracks that I never skip when it comes up. The lyrics at the beginning give it a momentum that carries through to the end: "my dewy-eyed Disney bride, what has tried swapping your blood with formaldehyde? Monsters? Whiskey-plied voices cried fratricide, Jesus, don't you know that you could've died, you should've died?"
49.
TV on the Radio -
Family Tree
Such a tender song. It's hard to believe that this is the same band that made
DLZ.
50.
Animal Collective -
Fireworks
This song is the ultimate jam when they play it live. It starts strong with a driving, train-like beat and doesn't let up.
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2. Murder by Death - Who Will Survive, and What Will Be Left of Them? (196) 
Broken Social Scene