There's already a great tab on the intro/verses here on UG. 
Though I thought I'd show you how I play it. 
It might not be 100% correct according to how OneRepublic play it, but this sounds good too.
Here's my suggestion to the song.

Intro/Verses:

e|--------------------------------------------|
B|--------------------------------------------|
G|--------------------------------------------|
D|--------------------------------------------|
A|----------5/7-------------------------------|
E|---0--0---------0--0--0--0---3b/0--3b/0-----|

Verse:
Hail Caesar shadow on my backseat 
And her friends are standing right in front of me 
World wide from the Cimmaron to Turkey 
Open up, said everybody loves me

C (x32010@1)                          AmAnd (x02210@1)you don't have to make a sound 
'Cause they got what you need, what you need 
Oh, oh, oh, oh

(Verse again)

Chorus:
E (022100@1)                      GOh (320003@1)my, feels just like I don't try 
               ALook (x02220@1)so good I might die 
              E7 (020130@1)All I know is everybody loves me 
E (022100@1)                      GHead (320003@1)down, swaying to my own sound 
              AFlashes (x02220@1)in my face now 
              E7All (020130@1)I know is everybody loves me

Everybody loves me

Bridge:
E (022100@1)And this is it for the rest of the song. :)