Key of D.

Verse/Chorus
1 - 1(3bass) - 4 - 5

Prechorus
2 - 2 - 5 - 1
2 - 2 - 5 - 5
2 - 2 - 5 - 6
2 - 2 - 5 - 5

End of Chorus
6 - 5 - 4 - 1(3bass) - 2 - 5 - 1

Great example of playing a chord that sounds like a 3 chord, but it's actually a 1 chord with it's 3rd in the bass   

Key of Eb

Main Song
1 - 3 - 4 - 5

Bridge Section (at 1:37)
4 - 4 - 4 - 4 (the arrangement is playing these as dominant)
1 - 3 - 4 - 5 

Last Repetition of this section
4 - 4 - (5of5) - (5of5)
5 - 5 - 5 - 5

Very similar to the Sheeran tune above, but noteably actually plays a 3 chord, as opposed to 1(3bass) 

Key of D.

Main progression
1 - 6 - 4 - 1
5 - 6 - 4 - 1

Also a great example of a 4 - 1 cadence 

Key of Db

Verse
1(3bass) - 5(3bass) - 6 - 4

That 5(3bass) also has a 6th in it (voicing is 3,1,5,6). Because of this, you could also call this chord a 3 chord, 5bass.

Prechorus
5 - 5 - 2 - 2
5 - 5 - 5----

Chorus
4 - 1 - 5 - 6

Great example of a song that has two different progressions that are actually the same thing, just rhythmically offset by a chord. The verse is 1-5-6-4, chorus is 4-1-5-6 which is the same exact number order, just starting on 4 instead of 1. 

Key of A

1 - 2 - 5 - 1

Doesn't get simpler.