Nick Reynolds of the Kingston Trio was a ukulele player, so when he switched to tenor guitar he tuned it like the top four strings of a standard guitar, DGBE. He often capoed to the fifth fret, making his tuning correspond to the uke. This is usually called "Chicago tuning". The great jazz guitarist Tiny Grimes also used this tuning. Today's tenor guitar players seem to be split between "Chicago" and "Standard" (CGDA) tunings.
PeterC.'s DGBD tuning is the same tuning as bluegrass 5 string banjo players use (minus the thumb string) and he's right that there are simple closed chord shapes that make transposing easy.
The tenor guitar seems to be making a come-back and many of the payers are using non-traditional tunings.
The plectrum guitar, an instrument similar to the tenor guitar, but with a longer neck and a different standard tuning (CGBD, I believe) was created at the same time as the tenor guitar to enable plectrum banjo players to switch to guitar with little or no learning curve. Eddie Condon was perhaps the most well known plectrum guitar player. Plectrum guitars, like plectrum banjos, are much rarer than tenors.