You can interpret it as the neutral option. One study reported negligible differences between the use of "undecided" and "neutral" as the middle option in a 5-point Likert scale. The value score you assign to it can be based on a desired level of detail. You can compute an overall score for a respondent's answer by simply summing the score for each item, or averaging the points for all nonmissing items. By doing so you assume that all the items in a scale have the same weight and that each item is measuring the same construct.
I think it depends on your question. Sometimes the midpoint is "neither agree nor disagree" but at other times it might mean more like "I don't know" (or even "I don't care")
If you haven't started your research, the other option is to include "I don't know" as another "point" on your scale. Only trouble then is that you have to decide what to do with those answers! :-)
If you need an "I don't know" option, then the particular item might not be appropriate for the intended participants, or it might be badly constructed or worded.
If for some reason you really want to have an uneven number of scale points with a point in the middle, then, in order to be able to interpret this, you must label this, just as you label the other values. This is because you cannot simply assume that each respondent will choose the middle point for the same reason. Some may choose it because they have no opinion, some because they don't know, and some because they see it as a neutral point. That being said, even if you do label the middle point as "neutral", say, you need to ask what information this provides,with respect to what you want to measures. What is essential is knowing BEFORE you use the scale, exactly WHAT you want to measure. Or to put it another way, you need to clearly define the construct before designing the scale. Once this has been done, one can manipulate and analyze these numbers accordingly. Thus, answers to questions such as how to weight the middle point, if at all, with respect to the other points on the scale, whether the middle point should be zero, or whether it should be the midpoint, 3, for example, on a scale from 1 - 5, all depend on how one has defined the construct.
I don't think anyone in this thread has mentioned that there is actually quite a large literature on the middle option. For example, I found this paper in about 10 seconds of googling:
And one of the findings that is relevant to this question (and Lyle's answers) is how participants interpret the middle response. Hernández et al. (2004) found that the middle response is a mixture of responses from people who are medium in their trait standing and others who are simply confused or who "don't know". They argue that this may be a serious problem for the interpretation of Likert scales if you have people who are confused but you scored their response as in the middle. If so, a solution may be to provide a separate "I don't know" or "Cannot decide" or "Not applicable" response option.
Hernández, A., Drasgow, F., & González-Romá, V. (2004). Investigating the functioning of a middle category by means of a mixed-measurement model. Journal of Applied Psychology, 89(4), 687.
Alan, thanks for digging and for the reference. (I think I did mention, in my first response, that there was a large literature on this, but I was too lazy to do the digging.) What you say and John's reply both underscore the problems in interpreting the results of Likert-type scales with middle responses.
Another issue that hasn't come up it that what type of scale, or level of measurement, these are. I use the term "Likert-type" scale because we can't really claim that these scales are interval, as Likert originally intended, until we've tried them out and done the necessary analyses to support this claim. Many studies that use "Likert" items do not report how these were developed before they were used, and I know from long experience that the necessary pre-testing and analyses are seldom done. Thus, we can't necessarily claim that the responses constitute a Likert scale. Unfortunately, graduate students in measurement seldom take a course that covers scale construction, and many graduate advisers do not require their PhD students to do the necessary scaling before they use these scales in their dissertation research. Of course, using a scale that was developed for a different study, with a different population, doesn't solve the problem.
So, in a nutshell, "just use a Lickert scale" isn't quite as simple as it may sound. FYI, I had a quick look at the Wikipedia entry for "Likert scale", and it's actually very informative for anyone interested in the issues.