First off, the passion in their music. It is something that is both strong and easy to hear. From the anger in P.L.U.C.K., to the nostalgia in Radio/Video, to the pain in Lonely Day. When I listen to them I can tell how much it means to them, and when Serj screams, its not some manufactured scream used by most screamo bands...its a real scream with real emotion
Next, the lyricism. I love the complex lyrics they use (most prominent in their first album). And what's best is sometimes a song doesn't sound like what it means. Vicinity of Obscenity is about their dislike for how people turn virtually everything into perversion. Jet Pilot is about animal abuse.
Another thing, their sound. They don't have a bland sound like most bands, not do they have 1 song that sounds nothing like them at all (which is usually most other bands' hit songs). All songs have their own distinct sound, while also able to be recognized as a SOAD song. And with their sound is their progression and change. They don't just stick to one sound, they change it up. Their first album (System of a Down) was more garage band sounding with focus on lyricism. 2nd album (Toxicity) was a more adrenaline pumped/pumping album, with focus evened between lyricism and music. 3rd album (Steal this Album!) is a more quirky album, with a more excited feel. And the dual album (Hypnotize/Mesmerize) was a more harmonic album, with a huge focus on melody and the music.
Lastly, the people involved. Serj Tankian is one of my top 3 idols (the other 2 being dead...aw so sad) and the messages he brings forward are so well made and so poetically created. Daron Malakian is awesome...he is fun, energetic, funny, but when he is off stage and just his normal self he is quiet, thoughtful, and deep (plus one hell of a guitar player). Shavo Odadjian (of course with that awesome goatee thing haha) is kind of like the chill guy of the group. And John Dolmayan, who always seems to have a serious face at all times while drumming (Serj tries to make him laugh alot while on stage because of this), and is someone who seems like he'd be a great friend, and someone you wouldn't want to mess with