The project I'm working on right now has undecidable problems all over it. It's a unit test generator, so in general what it tries to accomplish is to answer the question "what this program does". Which is an instance of a halting problem. Another problem that came up during development is "are given two (testing) functions the same"? Or even "does the order of those two calls (assertions) matter"?
What's interesting about this project is that, even though you can't answer those questions in all situations, you can find smart solutions that solve the problem 90% of the time, which for this domain is actually very good.
Other tools that try to reason about other code, like optimizing compilers/interpreters, static code analysis tools, even refactoring tools, are likely to hit (thus be forced to find workarounds to) the halting problem.
