<p>Each cell contains some text and a background color. So I have some cells that are blue and some that are red. What function do I use to count the number of red cells?</p>

<p>I have tried <code>=COUNTIF(D3:D9,CELL("color",D3))</code> with no success (Where <code>D3</code> is red).</p>

Excel has no way of gathering that attribute with it's built-in functions. If you're willing to use some VB, all your color-related questions are answered here:
http://www.cpearson.com/excel/colors.aspx
Example form the site:
The SumColor function is a color-based
  analog of both the SUM and SUMIF
  function. It allows you to specify
  separate ranges for the range whose
  color indexes are to be examined and
  the range of cells whose values are to
  be summed. If these two ranges are the
  same, the function sums the cells
  whose color matches the specified
  value. For example, the following
  formula sums the values in B11:B17
  whose fill color is red.
```
=SUMCOLOR(B11:B17,B11:B17,3,FALSE)
```