Working off the examples given by @Miles and @Siddarth Rout, I just created this variation. As a note, this is for the backend of an app that tracks user feedback, which needs to be presented broken out in different ways for a variety of audiences. While we wait for the developers to build the reporting end of the app, I'm downloading the data from SQL as a .csv, massaging the crap out of it in Excel, which then feeds 27 individual charts and graphs (soon to be 28 if we can get the final user group online!)
I went through and named each of the charts what I need the resultant files to be called so I can upload the graphics to the app server, overwriting the previous week's graphs, automagically (for the end users) updating the reporting.

Since the file names need to remain exactly the same, naming the graphs made the most sense, so I never need to touch that part again. (Until doing this today, I've been copying each chart, pasting into Paint, then saving as a PNG, and saving over the previous week's files so I could just click on the old one, which automatically assigns that name to the Save As process. Finding the code above and a way to make it even slicker will both save me about 30 minutes a week AND remove 27 possible manual errors... pretty good investment! If only I had made it... a year ago?)
' Ctrl-Shift-A to run
Sub ExportChart()
Dim WS As Excel.Worksheet
Dim SaveToDirectory As String
Dim objChrt As ChartObject
Dim myChart As Chart
SaveToDirectory = ActiveWorkbook.Path & "\"
For Each WS In ActiveWorkbook.Worksheets
WS.Activate 'go there
For Each objChrt In WS.ChartObjects
objChrt.Activate
Set myChart = objChrt.Chart
' Change from above: using ChartObject.Name to individually name each exported PNG file
myFileName = SaveToDirectory & objChrt.Name & ".png"
On Error Resume Next
Kill SaveToDirectory & WS.Name & Index & ".png"
On Error GoTo 0
myChart.Export Filename:=myFileName, Filtername:="PNG"
Next
Next
MsgBox "Eeeaaagle!!"
End Sub