The metalhead stereotype can be unforgiving. Based on the cacophony of growls, guitars distorted beyond recognition, and blast beats, you'd figure the people who enjoy listening to this dissonance must have seen some shit, or perhaps something's wrong with them to begin with. Totally understandable; metalheads acting like idiots regularly make the news. The vocalist of As I Lay Dying (right) was just arrested for allegedly plotting to kill his wife, some fans love Slayer so much they pause carving the band's name into their skin with knives (warning: slightly graphic) to spray pentagrams on tombstones in cemeteries, and a woman was raped in the mosh pit during the Limp Bizkit set at Woodstock 1999.
The aggression and energy of metal is frequently construed as the release of negative emotion. Yet, a lot of metal can be interpreted as happy or uplifting. Especially in progressive metal, the music often tells a story of "this is just the way it is," devoid of an angry message aimed at someone. Any aggression from the vocals or instruments merely adds weight to the story, the anguish of being mistreated or wailing at the illogical injustice of losing a loved one. Sometimes, the energy and intensity can be used to tell a positive or happy message, too, as I'll show below.
This or the Apocalypse - "Lamnidae"
Vocals: clean, shouting "Lamnidae" is one of my favorite metal songs. Here's a link to an (imperfect) drum cover I did of it two years ago. What I love about this song is the sense of positive energy you get from it, of camaraderie, going through a difficulty as brothers. The lyrics of the chorus are especially inspiring when coupled with the guitar (and the drummer effortlessly flipping the sticks): "Broken, relentless / Show them more heart than scars / Never give in / Stop holding your breath and start making your mark."
Between the Buried and Me - "Astral Body"
Vocals: clean, growling
Even with the growling at 1:38, the first half of this song just has such an optimistic, open feel. I particularly love 2:11, especially the 32nd-note bass drum rolls right before the hitting the snare, which give it more of a kick. The rest of the song alternates between neutral and aggressive tones, but for an album opener, the beginning of "Astral Body" has a lot of optimistic energy.
Intervals - "Mata Hari"
Vocals: none
It's really hard to write about music, especially instrumental pieces. "Mata Hari" is a guitar-driven story about... life? I envision daily life; the chorus is about that golden end point you're working towards, and the verses are about the daily grind (though quite a bit more epic than staring at a computer screen in an office). Perhaps it's easier to just listen to it and form your own conclusions. At 1:28, the distorted guitars undoubtedly have undertones of aggression, but I just get a feeling of optimism, like taking your energy and devoting it to pushing towards where you want to be. And slightly unrelated... but 2:36 is so awesome.
Killswitch Engage - "Holy Diver" (Dio cover)
Vocals: clean, shouting
Metal is all about intensity. While definitely awesome, this intensity shouldn't always be taken too seriously. Bands like iwrestledabearonce constantly poke fun at metal (while still delivering awesome metal) and others like Protest the Hero try to tell progressively more ridiculous stories in each of their music videos. Killswitch Engage covered the early 80's metal classic "Holy Diver" but kicked up the tempo and ridiculousness (especially in the music video). I can't help but find this stuff funny and awesome, a high-energy, apparently very serious song that's hilarious when you read the actual lyrics and picture trying to say them in any non-metal context (e.g. "Ride the tiger / you can see his stripes but you know he's clean / Oh don't you see what I mean?").
Notable mentions
Periphery - "Insomnia"
Vocals: clean, screaming, growling
Most of the song is high-energy, with plenty of screaming, guitar wizardry and crazy drums (just listen to the intro for awesome chaos). There is one riff, though, that I always feel describes an interesting sense of elation and freedom. The lead guitar from 2:18 - 2:30, particularly the rising notes at 2:23, has less of an aggressive and angry "fighting back" tone than... ecstatic, jubilant, free (at least, in my opinion!).
John Petrucci - "Glasgow Kiss"
Vocals: none
Vocals: none
You could argue that this is more rock than metal, so I've placed this under notable mentions. This is one of the most optimistic, happy metal songs I know. I really like how the drummer plays on the ride cymbal during the chorus (e.g. 0:14) and the odd-time at 2:30 (or is it 8/8?? I can't tell...).
Necrophagist - "Extreme Unction"Vocals: growling
I don't know, something about this song just makes me so happy, like playing peekaboo with babies or taking a puppy for a walk in a sunny field. (In all seriousness, I'd be very surprised to find a "happy" death metal song. I wonder if it's part of the definition. And side note: the way the vocalist's fingers move like spiders on the guitar neck while he's still growling the chorus at 1:47 is sick.)