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.
The four basic steps of any black box test are 1. Identify your oracles (How do you tell if something is a bug?), 2. Identify your "surfaces" (What are the variables that could change during testing?), 3. Identify your risks (What are the highest priority functions? - that will change as your testing progresses), and 4. Make a plan.
For oracles, do you have other devices to compare to? Do you have a list of formal requirements or an informal statement of how it should work?
For surfaces, is there any interface specifications or limitations? How is the RS-232 configured? What are the expected limits on the ADC?
For risks, what is the most important function to evaluate for now? Again, this will change as you get deeper into the testing.
For the plan, don't get fancy. Just figure out a set of tests that will cover the surfaces you identified in a reasonable amount of time. You probably want to start with some fast, basic steps and then expand from there as things appear to be working. (Tests never "pass", they just haven't been explored enough. Make it break!)
Hope that helps!