How to test embedded software running on a microcontroller?
I have developed a microcontroller application using an ADC, a RS232 port and some digital I/O.
How can I verify the application in black box fashion (not using development tools)? And are there any test tools for that?
Start by forgetting about the "micro-controller" and "embedded" parts and design tests like for any other system. Look at the specifications, explicit and implicit, and design tests o cover them.
Test tools ? there are a lot of test tools that match your general description and can generate analog signals, RS232 (even your PC can) or digital signals, you'll have to be more specific.