The sample rate of audio and video are two different things.
Video's Frames Per Second (fps)
In video, a frame (sample) rate of 24fps is required to prevent flickering. The common frame rates (25 and 30) has to do with the fact that early televisions used the mains frequency for the purpose of syncing (50Hz in the UK, 60HZ in the States). The primary reason for higher frame rates is the reduction of motion blur. To my knowledge, latest research suggests that somewhere between 90Hz-112Hz the effect is no longer recognisable.
Audio's Sample Rate
The sample rate of digital audio relates to the highest frequency captured/reproduced. As the Nyquist Theory states:
A signal can be perfectly captured and reconstructed, so long the signal is band limited and sampled at equal intervals at a frequency at least twice the highest frequency present.
Thus, a 44,100Hz sample rate can accommodate a signal with frequencies up to 22,050Hz. A 40000Hz sample rate can accommodate a signal with frequencies up to 20,000Hz
Following a debate, the 44,100 Hz figure was chosen as the best compromise between various requirements, including those of the various television standards at the time. This sample rate was subsequently used with audio CDs.
However, analogue-to-digital conversion (ADC) technology in the 1980s still exhibited distortion at levels that could be reduced using higher sample rates. Thus, when the DVD standard was established, the sample rate of 48,000 was chosen; representing a higher-fidelity audio.
The limitations in technology at the time are no longer part of modern ADC, where nearly all converters use 1-bit oversampling.
Human Hearing Range
The audible human hearing range is quoted as 20Hz - 20,000Hz (20kHz). Not a single empirical experiment in history has shown that any human being is capable of hearing frequencies above 20kHz. This is attributed to the density of the high-frequency 'hair' cells in our ears and the maximum rate at which they fire.
It is also worth noting that about more than half the population above the age of 45 is incapable of hearing frequencies above 16kHz.
Inaudible Frequencies can Yield Audible Ones
However, any signal being converted from digital to analogue must pass through a non-linear system before it reaches our ears. The obvious example of such system is the speaker cone. When audio passes through a non-linear system, distortion is created in the form of additional frequencies. Under such conditions, frequencies above 20kHz can actually result in distortion below 20kHz. However, unless the non-linear system is fundamentally faulty, for programme material (normal typical everyday sounds - not a loud sin wave of 30kHz) the distortion created is inaudible.
The same principle applies when digital audio is processed in a non-linear fashion within a digital system. Distortion content above 20kHz will be generated, and depending on the sample rate, it may alias back to the audible range.
The last two paragraphs explain why it is sometimes justified to use sample rates higher than 44,100.
ADC Frequency Headroom
To answer your question directly, the required limit of sampling rate (while only accounting for human hearing) is 40,000Hz.
However, before sampling, convertors need to filter audio content above 20,000Hz. Since the effect of all filters is gradual (they cannot simply remove everything above a particular frequency, they only attenuate it gradually), convertors need some headroom to sufficiently remove content above 20,000Hz. Thus, a sample rate higher than 40,000Hz is always required.
While 40,000Hz represents the theoretical max sample rate required with humans, ADC technology still requires some headroom above this figure.
With modern ADC technology, 44100Hz is perfectly capable of capturing material up to 20,000 Hz.
From a game development point of view, you should not worry about this aspect.