Muttley,

You asked for hymns that move us. How about "I heard the voice of Jesus say/Come unto me and rest"? Or

"Ah, holy Jesus,
How hast Thou offended
That man to judge Thee
Hath in hate pretended?
By foes derided,
By Thine own rejected,
Ah, most afflicted."

(And it goes on from there)

The last verse of "Lo, How a Rose" always gets to me as well:

"Oh flow'r whose fragrance tender
With sweetness fills the air,
Dispel, in glorious splendor,
The darkness everywhere.
True man, yet very God,
From sin and death now save us
And share our ev'ry load.