We all know when testing you try the minimum, maximum, something in the middle, one plus the max, one minus the minimum and maybe a couple interesting values.
When testing an administrative application, I ran into a critical failure at the system level when the domain name was exactly 26 characters long. The minimum was 3, the maximum (in this case) was 64 due to other system restrictions and I stumbled upon this problem after a previous version of the system had been tested and released containing this bug.
After investigating and discussing the bug with the developer, the system call was initially guessing and only allocating 26 characters, it would get a failure if the buffer wasn't big enough and from the failure code it would then know how much memory to allocate, but at that undocumented initial buffer guess boundary the initial conditional statements were a bit off, > rather than >=, so the system came to a crashing halt.
I have to say, as a tester, this type of thing is very frustrating. I really want to help my developers find the bugs before we release, but hidden magic numbers like this aren't usually found without exhaustive testing and we never have time for exhaustive testing.