I'm sure it's copying some kind of hospital sound effect, like an old-tech intercom tone or a warning buzzer, but I just cannot fucking place it. I know I know this sound.
It's driving me nuts. Can someone please tell me what it is? Bonus points if you can link to a recording.
Sounds like a flute combined with a lot of EQ, leaving only the mids with no attack. This is accompanied with the occasional string pluck of what seems like a guitar. Same EQ, which makes the two instruments blend together in an etherial kind of way. Slap some spring reverb on top.
EDIT: The strings sounds like the overtones of a half acoustic guitar. I think the vibrato is artificially applied. It's kind of possible to make that effect by slapping the whammy bar, but not in a way that'd make it fade in like that. Maybe if you lightly touch the already vibrating string in the right spot you could achieve something like that, but I'm unsure if it'd work, or if it'd create an overtone on an overtone.
UPDATE: Yup, I just tested it. Those are definitely overtones of a guitar. I couldn't replicate the vibrato, so I'm pretty such that's been applied in post.
As a tangent, I watched all of House from start to finish when each episode was released by EZTV. As a result, I only ever heard the american intro despite being European. I didn't even know other intro songs existed until now. I guess they didn't have international distribution rights to Teardrop.