I am pretty sure that these chords are right. Most of the other versions on here seem to 
have the right structure for the verse and chorus but not for the prechorus or bridge. 
(At least in my opinion :D)

This also sounds great if you tranpose it to a Capo 5, if you're more partial to open chords.

This is one little ditty here in the verse that I wasn't sure how to tab in. After you 
land on the F and before you go to C play this:

e|------1----------0-----------|
B|------1----------1-----------|
G|------2-2-3-2-0--0-----------|
D|------3----------2-----------|
A|------3----------3-----------|
E|------1----------------------|

 You can distinctivly hear this in the piano and I think it makes the guitar sound a lot better.

         Dm       F
I let it fall, my heart,
          C                Gm
And as it fell you rose to claim it.
       Dm                 F
It was dark and I was over,
          C                       C
Until you kissed my lips and you saved me

Verse
    Dm            F
My hands they're strong,
         C                 Gm
but my knees were far too weak,
  Dm           F
Stand in your arms
         C                  C
without falling to your your feet,

Prechorus:
              Bb                   Gm
But there's a side to you that I never knew, I never knew.
           Dm                                 Dm
All the things you'd say, they where never true, never true,
          Bb         Gm              C
And the games you'd play, you would always, always win.

Chorus:
           Dm
But I set fire to the rain,
         C
Watch it pour as I touched your face,
     Gm
well it burned while I cried,
          (Am)                      Dm          C
Cause I heard it screaming out your name, your name

      Dm        F
When I'm with you
    C
I could stay there,
 Gm
Close my eyes,
              Dm     F
feel you're here forever,
          C
You and me together, nothing is better!

Prechorus:
              Bb                   Gm
But there's a side to you that I never knew, I never knew.
           Dm                                 Dm
All the things you'd say, they where never true, never true,
          Bb         Gm              C
And the games you'd play, you would always, always win.

Chorus:
           Dm
But I set fire to the rain,
         C
Watch it pour as I touched your face,
     Gm
well it burned while I cried,
          (Am)                      Dm          C
Cause I heard it screaming out your name, your name!
I set fire to the rain
And I threw us into the flames
And it felt something die,
Cause I knew that that was the last time, the last time!

Bridge:
         Bb                Am
Sometimes I wake up by the door,
         Am                          C
That heart you caught, must be waiting for you,
     Bb                      Am
Even now when we're already over,
     Am                            C
I can't help myself from looking for you

[Chorus: ]
I set fire to the rain,
Watch it pour as I touch your face,
well it burn when I cry,
Cause I heard it screaming your name, your name
I set fire to the rain,
And I threw us into the flames
Cause I knew that was the last time
The last time, oh, oh!

Chorus Chords:

Let it burn!

Let it burn!