I’ve been taking singing lessons for awhile and the classes are split up 50/50 with the first half being vocal and ear training and the second half working on a song I bring in. I usually sing along with the CD at first which includes changing the key and then I play without the CD and just my guitar. The issue is a touch psychological as when we lower the key to something more suited for my voice, I start singing it a bit…well, dirge-y. Once I play it a couple times without the CD and just the guitar, I’m fine, but it’s the familiarity with the song that makes me want to slow it down since it’s lower. So, long story short, who are some good/great baritone singers and their songs?
There’s an old Harry Chapin song called “Mr. Tanner”, in which there’s a barotone solo in the middle. Harry was a tenor, not a baritone - but one of his band members sang it. Here are part of the lyrics:
It’s a great song, typically Harry Chapin.
StG
I don’t know how you feel about country, but there are Trace Adkins and Josh Turner, both with great baritone voices.
Michael Buble is a baritone or bass baritone. There was this guy named Sinatra, he was a baritone too. 
Stephin Merritt of the Magnetic Fields, in addition to being the greatest living songwriter, is a hell of a baritone. Listen to just about anything here , like “I don’t believe in the sun” or “I don’t want to get over you.”
I don’t know if he qualifies as modern, but Johnny Cash was a great one in my opinion.
Ian Curtis (Joy Division) was bass-baritone
If you’re into rock music, try some Social Distortion, or Mike Ness solo albums. SD’s best-known song is probably “Ball and Chain,” and it reflects Ness’ baritone range well.
Anything by Johnny Hartmann.