whenever the sampling theorem was explained to me, a situation of this kind was proposed to me.
If we look at the previous image we will see that the condition to avoid spectral aliasing is that we have
\$f_S \gt 2 f_0\$
But now let's consider this specific situation (which corresponds to a pure sinusoidal signal):
or also a more general situation in which there is a certain bandwitdth on the positive frequency axis. In this case, which is the condition to avoid aliasing?
The sample rate needs to be greater than (not greater than or equal to) twice the maximum frequency of the signal of interest. As @Michael pointed out, sampling a sine wave of exactly 100Hz with a sampling frequency of exactly 200Hz results in data that is indistinguishable from dc.
Reconstructing the input sine wave requires a filter on the output values, not on the input side. (The filter on the input side is for anti-aliasing, another matter entirely.) Ideally, both filters would be brick-wall filters at the Nyquist frequency. See reconstruction filters.
All the answers given so far are incorrect. The Nyquist sampling rate only applies for a lowpass signal. With a bandpass signal you can utilize what is known as undersampling.
If you sample a band limited signal occupying the bandwidth \$f \in [f_L, f_H]\$ at some frequency \$f_s\$, you will get the expected repetition in the frequency domain.
If you are careful about your sampling frequency, you can avoid aliasing without needing to sample at the Nyquist rate for a lowpass signal. The sampling frequency must satisfy
$$f_s \in \left( \frac{2f_H}{n}, \frac{2f_L}{n-1} \right)$$
where \$n \in \mathbb{N}\$ is a natural number such that
$$n \leq \left\lfloor \frac{f_H}{f_H - f_L} \right\rfloor.$$
Note that \$f_L = 0\$ yields \$n = 1\$, which gives you the Nyquist sampling rate
$$f_s \in (2f_H, \infty).$$
Nobody has mentioned the duration of the sampling. For ideal reconstruction, the samples need to be taken at a rate above twice the band-limited bandwidth. How far above twice the bandwidth depends on the duration of the sampling. Sampling infinitesimally above the Nyquist rate is only good for infinite length sampling (e.g. you started before the Big Bang). Realistically, the time limited window of your samples corresponds to a rectangular time window, which spreads the windowed signal out in the frequency domain. So the sample rate needs to be higher to account for that windowing spread of bandwidth.
For narrow-band signals in zero noise, even at very high frequencies, you can sample at only somewhat above twice the bandwidth, e.g. for a 100 MHz signal with no more than 10 kHz of bandwidth (and absolutely nothing in the total signal outside that bandwidth), you can probably get away with sampling at 33 to 40 kHz, or maybe at a lower rate towards just above 20 kHz if you sample for a very very long time. No need to sample somewhat above 200 MHz, unless your band-limiting filter goes bad, and noise outside the 10 kHz bandwidth leaks in.
In order to avoid aliasing, according to Nyquist, you need to sample at a frequency of at least twice the value of the highest frequency you wish to measure. For your sinusoidal input, there is ideally only frequency content at the 100Hz mark, meaning you need to sample at 200Hz minimum for no aliasing to occur.
Do keep in mind however, if you sample at 200Hz, you only sample the sine wave twice per period, meaning that depending on where those samples fall, you may measure drastically different values. For example, if the samples fall on the zero crossings of the sine, you would measure 0V DC. Sampling 5-10 times the highest frequency helps ensure that your sampling produces a more accurate representation of your initial signal.
In addition to Michael's answer:
In order to reconstruct the signal uniquely and accurately from samples taken at just above the Nyquist frequency, you need to interpolate those samples to increase the number of points which will give you a distorted waveform.
Then you run those points through an IDEAL low-pass filter with a 100Hz cutoff to remove all the high frequency junk introduced by the interpolation method (since you know your original's signal bandwidth so you know that any frequency components above that should not be there).
Of course, such an ideal filter does not exist so in practice you have to sample much faster than the Nyquist frequency.
Sampling at Nyquist just stops high frequencies from aliasing into into your samples. It doesn't stop high frequencies from sneaking back into the signal somewhere down the line during reconstruction.
