What planets are visible to the naked eye from Mars?

Aside from having Earth visible in the night sky instead of Mars, you would expect the same planets to be visible.

• Venus will appear as a bright star close to the sun - smaller than we see it, but still very bright.
• Jupiter and Saturn will be easier to see in the night sky, and it should be possible to pick out Jupiter's four major moons with the naked eye.
• Uranus is going to be interesting. while Mars will get closer to it than Earth, as Rob points out, the dust in the MArtian atmosphere will remove the possibility of seeing Uranus.
• Neptune will still be invisible to the naked eye.

You will see Earth, Venus, Jupiter, Saturn. They are either bright enough, or come closer to Mars than Earth, that there are no complications/calculations necessary.

Uranus is just a naked eye object from Earth (magnitude 5.3-5.9). Its closest approach to Earth, when it is brightest is 17.2 au distant. Mars' orbit takes it closer by about 0.5 au, so you might have thought it would be more visible. But no - on average the visual extinction in the dusty atmosphere of Mars is around 0.5-1 astronomical magnitudes (see this relevant Astronomy SE answer) and this means the gain due to proximity (about 0.1 mag) is wiped out by the extinction. You would be very unlikely to see Uranus unless you had exceptional vision and knew where to look when Uranus was at its brightest.

Mercury is tricky. It is certainly bright enough to be seen from Mars, but would be sepated by a smaller angular distance from the Sun. The contrast between Sun and Mercury would be the same. I think on balance, it would be visible if you looked carefully, since Mercury can be seen from Earth when it is closer to the Sun than its maximum angular distance, though the Martian atmosphere might affect the glare from the Sun differently.