In general, you are probably infringing our trademark if you use one of our logos in your product, because it would be likely to cause confusion as to the origin of your product, so I would advise against it.
Technically, if the logo was used in a way so that it didn't look like a part of your application, and didn't cause confusion, there might be a "fair use" claim. For example, if you make a help page available, and your help page includes a screen shot of Stack Overflow that is obviously a screen shot of Stack Overflow, nobody is likely to be confused that you are in some way associated with Stack Overflow or approved by Stack Overflow.
We're going to work on getting some logo/trademark guidelines up that make sense.