Here are just a few flavors.
Among the earliest I could find is "Me and My Uncle," from 1965 (mentions Texas!):
A few years later, one of her earlier hits in her sweet young voice: "Chelsea Morning"
Then a favorite of mine, in a live performance, "Free Man in Paris":
Now a more mature Joni delivers a very jazzy, playful tune that showcases her range, in "The Dry Cleaner from Des Moines":
Unfortunately there's no video to this, but Joni's voice lends itself nicely to a lovely version of "Why Do Fools Fall in Love?"
Finally: not a big Elton John fan, but here at a Joni Mitchell tribute he turns in a good, somewhat more melancholy cover of "Free Man in Paris":