Once i spent some time jaming on my acoustic and found a good way to play this song. 
Mode songs make good acoustic versions - Personal Jesus is one of my favourites!

The song is in Am

Main riff:

E|------------------------------------------|
B|------------------------------------------|
G|------------------------------------------|
D|-----------7-------------7----------------|
A|-7--7--7-7-7---7--7--7-7-7---7--7--7-7-7--|
E|-5--8--5-5-5---5--8--5-5-5---5--8--5-5-5--|

This Riff Is very simple. Just play the A5 on the 6th string and add the C on the 8th 
with your little finger. You can also play the full chord but it doesn't sound better.

Chorus:

E|---10-10-10-/-1-1-1-\-3-3-3-\---------------------------------|
B|---10-10-10-/-1-1-1-\-3-3-3-\---------------------------------|
G|---10-10-10-/-2-2-2-\-4-4-4-\---------------------------------|
D|-12---------/3------\5------\10-10-10--10-------------------7-|
A|-12---------/3------\5------\10-10-10--10------7--7--7--7-7-7-|
E|-10---------/1------\3------\8--8--8---8----5--5--5--8--5-5-5-|

This part may be the most difficult. If you're good at chords, you'll pick it quickly. 
trickiest part is the bridge from C5 to main riff. Notice the slides.

Bridge:

E|-----------------------------------2--2--2-2-2-1--1--1-1-1-----------|
B|-----------------------------------2--2--2-2-2-1--1--1-1-1-----------|
G|-----------------------------------3--3--3-3-3-2--2--2-2-2-----------|
D|-12--12--12-12-12-10--10--10-10-10-4--4--------3--3------------------|
A|-12--12--12-12-12-10--10--10-10-10-4--4--------3--3--------------7-7-|
E|-10--10--10-10-10-8---8---8--8--8--2--2--------1--1--------\-8-5-5-5-|

Outro:

E|--------------------------------------------|
B|--------------------------------------------|
G|--------------------------------------------|
D|-----------7--------------------------------|
A|-7--7--7-7-7------7--7--7-7-----------------|
E|-5--8--5-5-5------5--5--5-5-5-\-12~~~~------|