There's quite a bit of fan art out there for just about every property under the sun, and Barsoom has it's own fans--student, pro, and everyone in between. Here's a few of my recent favorites:
I dig the ridged skelatal structure beneath the skin of this Thark character sketch by student Brennan "tehnoochness' Wagner.
Professional illustrator Adam Moore, a.k.a. Laemeur's, "Earth Astride Mars" depicts a pivotal scene in A Princess of Mars, when John Carter has frankly had enough of Tharkian boorishness.
I REALLY dig this sketch of Tars Tarkas by aquilianranger (first name Scott?). I love when people go all insectoid with their Tharks. This guy is dying to be in an RPG or an awesome illio for somebody's Thri-kreen character.
Also, for some reason he sorta reminds me of another badass bugman...
Finally, we have a great shot of the three heroes from A Princess of Mars., Tars looks particularly dashing with blades at the ready and soulless, ebony shark eyes. This one's by Ryan Valle, also known as Praxiteles: