In America it began to appear in surf music of the early '60s followed by the spaghetti westerns made famous by Clint Eastwood. Glen Campbell and Carol Kaye used it for Jan and Dean recordings.
Country music starting using it as a tic-tac bass that doubles their bass.
Also it began to stand out as a solo guitar such as Sara Evans' "Suds in the Bucket" and Lee Ann Womack's "A Little Past Little Rock."
The song most played in the last millennium on radio was Glen Campbell's "Wichita Lineman" that featured the baritone.
Basically the guitar has a longer scale length than a normal guitar. Somewhere between 27 inches and 30.5 inches. The longer one allows lower tunings such as A D G C E A which is a fifth lower than standard tuning. The shorter scales are usually tuned a major 3rd or perfect 4th, C F Bb Eb G C or B E A D F# B respectively. The string gauages used vary from .012 - .054 to .017 - .095.
Artist who popularized the guitar in their songs were:
1. Duane Eddy - songs "Bonnie Came Back," "Because They're Young," "Kommotion," "My Blue Heaven," "Deep in the Heart of Texas," "The Rebel Rouser."
2. Brian Wilson used it in songs "Dance, Dance, Dance," "Caroline No."
3. Jimmie Rogers song "Woman From Liberia."
4. Glen Campbell songs "Wichita Lineman," "Galveston" and a host of others.
Heavy metal groups have used it especially with drop tunings. Rock groups such as Aerosmith, Dave Mathews, Staind. Jazz musicians Pat Metheny, Linda Manzer, Ani Di Franco and Clifton Hyde.
The baritone that has the deepest bass sound is the longer scale length 30 inches, tuned a fifth lower to A D G C E A. Although it is a 5th lower, the chord shapes remain the same, however at a 5th lower than standard an A becomes the E chord shape, G becomes the D chord shape and so on. It is easy to convert, simply count up, starting at the chord for standard tuning, five notes such as B, B is 1, C is 2, D is 3, E is 4, F is 5, so B becomes the F chord shape. The sharps get a little trickier since you are dealing with half spaces but it is not too difficult.
I find that while some chords sound really cool played as open chords with that really low bass sound, sometimes it is a little too much bass and the chord played as a barre chord sounds better. Sometimes played even 2 octaves higher on rare occasions.
Soloing on the guitar at the low end gets strange sometimes as the frets are so widely spaced, yet that is where the guitar shines with the tremendous bass sounds. Playing scales will take a little work with the muscle memory in your hand also because of the larger fret spaces.
You can use a capo device on the guitar. If your guitar is tuned to A, you will place the capo at the seventh fret to make the chord shapes used with a standard tuned guitar.
Almost all the guitar manufacturers are producing some form of baritone guitar and even in acoustic versions. Guild has an excellent acoustic as does Taylor. They usually incorporate two additional strings that are an octave above for the 3rd and 4th strings that gives it an almost 12 string sound.
If you are considering a baritone guitar I hope this was useful to you in your decision. I find it a rewarding instrument with the ability to broaden my playing.