Are there rule of thumb regarding sample size when neuroscientific measurements are used? According to this paper, 10-25 subjects are enough for an fMRI study. 
However, regarding EEG, it only mentioned in this paper that some "authors concluded that the relatively small sample sizes (average 20 subjects) in these studies are likely responsible for the inconsistent result". This paper did not give a recommendation of sample size.

Are there a rule of thumb regarding how many subjects should be used for neuroscientific measurements in general? Are there papers regarding this?

Note that I am not currently designing an experiment, but writing a literature review regarding application of neuroscience. So I don't think I can conduct a power analysis as an answerer suggested.
The minimum sample size required to plausibly reject the null hypothesis depends not on the area of study (e.g. neuroscience), but on your study design and the statistical tests you perform.

What you need to do is a power analysis. Questions regarding power analysis have been asked on Cross Validated. You may want to read up on power analysis in your favourite statistics textbook and, if you have questions, ask them there.