I've read that using log scales when charting/graphing is appropriate in certain circumstances, like the y-axis in a time series chart.  However, I've not been able to find a definitive explanation as to why that's the case, or when else it would be appropriate.
Please keep in mind, I'm not a statistician so I may be missing the point altogether and if that's the case I'd appreciate direction to remedial resources.
This is a very interesting question, and one that too few people think about. There are several different ways that a log scale can be appropriate. The first and most well known is that mentioned by Macro in his comment: log scales allow a large range to be displayed without small values being compressed down into bottom of the graph.

A different reason for preferring a log scaling is in circumstances where the data are more naturally expressed geometrically. An example is when the data represent concentration of a biological mediator. Concentrations cannot be negative and the variability almost invariably scales with the mean (i.e. there is heteroscedastic variance). Using a logarithmic scale or, equivalently, using the log concentration as the primary measure both 'fixe' the uneven variability and gives a scale that is unbounded on both ends. The concentrations are probably log-normally distributed and so a log scaling gives us a very convenient result that is arguably 'natural'. In pharmacology we use a logarithmic scale for drug concentrations far more often than not, and in many cases linear scales are only the product of non-pharmacologists dabbling with drugs ;-)

Another good reason for a log scale, probably the one that you are interested in for time-series data, comes from the ability of a log scale to make fractional changes equivalent. Imagine a display of the long-term performance of your retirement investments. It (should) be growing roughly exponentially because tomorrow's interest depends on today's investment (roughly speaking). Thus even if the performance in percentage terms has been fairly constant a graph of the funds will appear to have grown most rapidly at the right hand end. With a logarithmic scale a constant percentage change is seen as a constant vertical distance so a constant growth rate is seen as a straight line. That is often a substantial advantage.

Another slightly more esoteric reason for choosing a log scale comes in circumstances where values can be reasonably expressed either as x or 1/x. An example from my own research is vascular resistance which can also be sensibly expressed as the reciprocal, vascular conductance. (It is also sensible in some circumstances to think of the diameter of the blood vessels which scale as a power of resistance or conductance.) Neither of those measures has any more reality than the other and both can be found in research papers. If they are scaled logarithmically then they are simply the negative of each other and the choice of one or the other makes no susbstantive difference. (Vascular diameter will differ from resistance and conductance by a constant multiplier when they are all log scaled.)
