Definition of NMR peak In NMR a spectrum consists of noise and peaks. While steps, such as repeated scans or smoothing of the spectra can reduce noise some still remains. As such one step usually taken is to bin the data so that only peaks are chosen, usually with a threshold and finding maxima/minima.
This raises the question however, which is how do you define a peak. If you use a threshold a poor baseline can result in this failing, for instance if the baseline is above the threshold set.

Is there a widely used method/rule of thumb which is used to decide if a region contains a peak, or is just noise?
A general term used in all analytical chemistry is the lower limit of detection (LoD), which is generally defined as 3 times the standard deviation of the baseline/blank. So if you calculate the $\sigma$ standard deviation of the baseline in question, and you have a signal that is over $3 \sigma$, you can generally accept that as a peak. This comes down to the so-called 68-95-99.7 rule, according to which there is only a 0.3% probability that a peak higher than the LoD is an artifact.