According to Wikipedia...
Ideally, unevenly spaced time series are analyzed in their unaltered form. However, most of the basic theory for time series analysis was developed at a time when limitations in computing resources favored an analysis of equally spaced data, since in this case efficient linear algebra routines can be used and many problems have an explicit solution. As a result, fewer methods currently exist specifically for analyzing unevenly spaced time series data.
A common approach to analyzing unevenly spaced time series is to transform the data into equally spaced observations using some form of interpolation - most often linear - and then to apply existing methods for equally spaced data. However, transforming data in such a way can introduce a number of significant and hard to quantify biases, especially if the spacing of observations is highly irregular.
However, don't fret, there are plenty of ways to analyze irregularly-spaced time series data. Some of them are definitely better than others, depending on the outcome you would like to observe (theoretical relationships between variables, predictive ability, etc.). This PDF gives a decent mathematical basis for the problem you are struggling with.
If you like using MATLAB, you may find this intro to resampling helpful. The example explains how to resample nonuniformly sampled signals to a new uniform rate.
You also may find some of the R packages at the end of this whitepaper helpful, particularly the packages mentioned in section 7.