12. The Wheel
Pretty easy one to start things off.
Part of Futurama's core mythology is that they have evolved beyond the use of the wheel, something which gets specific focus in Mother's Day, where no one beyond Fry even knows what one is.
In Mother's Day, Mom begins a robotic uprising, causing all technology to rebel and leaving the incredibly dependent humans to fend for themselves. Fry then 'invents' the wheel (albeit a rather ineffective oval shaped one) to help cart the Planet Express crew around.
The Professor is even astounded, asking Fry to "'show us this 'the wheel'", confirming that not only are wheels not in use, they're completely unheard of.
However, wheels very plainly do exist within Futurama's world. While yes, cars have been replaced by hover cars, other wheels are extremely common in New New York.
We see office chairs, Bender's friend Fender (the one who gets him hooked on jacking on), and the Professor has several wheeled gadgets. When Bender bends him backwards, he uses a mini unicycle to support his head, and he has a wheel chair, one he specifically refers to as 'the one with the wheels'.