Under what circumstances is an N < 30 acceptable? I am doing some research in which I want to expose subjects to an "unusual" event and record their response. I am recording the subjects' responses via a sensitive brain instrument, so I've been told that exposing them to the stimulus 30 or more times is desirable. However, because the event is meant to be "unusual", I worry that its happening 30+ times during the experiment may lead to a distortion of the results.
Is it possible to get at my N by having more subjects rather than more events per subject?
If not, under what circumstances is an N < 30 acceptable?
 A: This is an answer to the general question about 30 being enough.
There is nothing magical about the number 30, it is just a rule of thumb that has been used for years in introductory stats classes.  It is a number and rule of thumb that really should be abolished (and I am speaking as a teacher of intro stats where the course notes use the 30 rule of thumb).
Part of the problem with that rule of thumb is that 30 is seen as the magic number that allows us to use tools that are based on the normal distribution, but 30 is just a nice round number that works in many cases, but there are many cases for which 10 or even 5 would be enough and other cases where 100 is still to small to have approximate normality.  So it really depends on your situation rather than a magic round number.
And even then, that is just if you want to use normality based tests, but there are many tests available that do not require a normal distribution (they just are not generally the main focus of an introductory class), so even with sample sizes that are to small for approximate normality, there are still ways to analyze the data.
Another big problem with the rule of thumb is that it often focuses the attention in the wrong direction.  More important that getting above a magic 30 to get approximate normality (as mentioned above other tools mean that is not needed) is the power of a test, which depends on many other facts.  A sample size large enough to give the approximate normality may still have less chance of finding a meaningful difference than flipping a coin.
Another issue to consider is that different measurements on a single subject will give different information than single measurements on different subjects.  Often adding one additional subject will give much more information than adding 10 additional measurements on each of the current subjects.
You really need to consult with a local statistician who can help you work through all the details to design the best study.  You may need to do this in a few different parts, first a pilot study with a few measurements on a few individuals to get an idea of how much variation there is within subjects and between subjects; this information can then be used to design a better study to answer your main question.
A: If a minimum N of 30 is being recommended per participant, I'm assuming there is a fair bit of noise in the instrument's readings, so you will definitely need plenty of measurements.
However, you are correct in your gut-reaction about exposure to your "unusual" event; you should not expose your participants to that event 30+ times.  Instead, you should use a very strong set of control data.  Expose your participants to non-"unusual" events many times, and only expose your participants to the "unusual" event once (or how ever many times makes sense).
Due to the implied measurement noise, you will probably need to do this over a decently large number of participants, but I would start by taking a smaller sample of participants and seeing just how much of a difference your "unusual" event produces.  If the effect is large enough, you may not need very many participants, but it will all depend on the variation in results.
I suppose the answer to your question "under what circumstances is an N < 30 acceptable?" is this: It's acceptable when the effect of your stimulus on your outcomes is obvious.  We wouldn't have to take a large sample to find that an explosion without warning causes surprise in people nearby, but we might have to take a very large sample to prove that the presence of a guitar at a symphony is surprising to the attendees.
