I think that all other versions have some mistakes either in the chords of the bridge or 
the Intro-Tabs. So here's what I think sounds authentic.

For the sake of playability I transposed it from A to G, hence Capo 2 ;)
My Immortal  (Capo 2)

[Intro]
    G                  Bm                 G                 Bm
e|-----3---7---3----|----------7-------|-----3---5---3----|---------7--------|
B|---3---3---3---3--|-----7-—----------|---3---3---3---3--|-----7-—----------|
G|-4----------------|---7---7----------|-4----------------|---7---7----------|
D|------------------|-9----------------|------------------|-9----------------|
A|------------------|------------------|------------------|------------------|
E|-3----------------|-7----------------|-3----------------|-7----------------|

[Alternative Intro]
   G                   Bm                 G                 Bm
e|------------------|------------------|------------------|------------------|
B|------------------|-------—--0-------|------------------|---------0--------|
G|---------4--------|------------------|------------------|------------------|
D|-----5-------5----|-----4------------|-----5---7---5----|-----4------------|
A|---5---5---5---5--|---5---5----------|---5---5---5---5--|---5---5----------|
E|-3----------------|-7----------------|-3----------------|-7----------------|

[Verse]
G                        Bm
   I'm so tired of being here
G                         Bm
   suppressed by all of my childish fears
G                           Bm
   and if you have to leave - I wish that you could just leave
G                                         Bm
   'cause your presence still lingers here - and it won't leave me alone

[Pre-Chorus]
Em     Bm                           Em
      These wounds won't seem to heal
       Bm                      Em
      This pain is just too real
       Bm                         D               (Em)
      There's just too much that time cannot erase

[Chorus]
Em           C         D        Bm               (Em)
   When you cried I'd wipe away all of your tears
Em               C        D         Bm              (Em)
   When you'd scream I'd fight away all of your fears
Em      C         D           Bm                (Em)
    I  held your hand through all of these years
Em            C   D
   But you still have     all of me

[Instrumental]
   G                  Bm                  G                 Bm
e|-----3---7---3----|----------7-------|-----3---5---3----|---------7--------|
B|---3---3---3---3--|-----7-—----------|---3---3---3---3--|-----7-—----------|
G|-4----------------|---7---7----------|-4----------------|---7---7----------|
D|------------------|-9----------------|------------------|-9----------------|
A|------------------|------------------|------------------|------------------|
E|-3----------------|-7----------------|-3----------------|-7----------------|

[Verse]
G                           Bm                              
   You used to captivate me   by your resonating light
G                           Bm
   but now I'm bound by the life you left behind
G                      Bm
   Your face it haunts    my once pleasant dreams
G                            Bm
   your voice it chased away   all the sanity in me

[Pre-Chorus]
Em     Bm                           Em
      These wounds won't seem to heal
       Bm                      Em
      This pain is just too real
       Bm                         D               (Em)
      There's just too much that time cannot erase

[Chorus]
Em           C         D        Bm               (Em)
   When you cried I'd wipe away all of your tears
Em               C        D         Bm              (Em)
   When you'd scream I'd fight away all of your fears
Em      C         D           Bm                (Em)
    I  held your hand through all of these years
Em            C   D               C
   But you still have     all of me

[Bridge]
C              Em             Bm               C
I've tried so hard to tell myself that you're gone
      Am7               Bm      C           D          Em
but though you're still with me I've been alone all along

[Instrumental]
| Em   C   D  Bm |  
| Em   C   D  Bm |  

[Chorus]
Em           C         D        Bm               (Em)
   When you cried I'd wipe away all of your tears
Em               C        D         Bm              (Em)
   When you'd scream I'd fight away all of your fears
Em      C         D           Bm                (Em)
    I  held your hand through all of these years
Em            C   D               (G)
   But you still have     all of me

[Outro]
    G                  Bm                 G                  Bm
e|-----3---7---3----|----------7-------|-----3---5---3----|---------7--------|
B|---3---3---3---3--|-----7-—----------|---3---3---3---3--|-----7-—----------|
G|-4----------------|---7---7----------|-4----------------|---7---7----------|
D|------------------|-9----------------|------------------|-9----------------|
A|------------------|------------------|------------------|------------------|
E|-3----------------|-7----------------|-3----------------|-7----------------|