Most of us know that a loop should not have a non-terminating condition. For example, this C# loop has a non-terminating condition: any even value of i. This is an obvious logic error.

void CountByTwosStartingAt(byte i) { // If i is even, it never exceeds 254
    for(; i < 255; i += 2) { 
        Console.WriteLine(i);
    }
}

Sometimes there are edge cases that are extremely unlikeley, but technically constitute non-exiting conditions (stack overflows and out-of-memory errors aside). Suppose you have a function that counts the number of sequential zeros in a stream:

int CountZeros(Stream s) {
    int total = 0;
    while(s.ReadByte() == 0) total++;
    return total;
}

Now, suppose you feed it this thing:

class InfiniteEmptyStream:Stream
{
    // ... Other members ...

    public override int Read(byte[] buffer, int offset, int count) {      
        Array.Clear(buffer, offset, count); // Output zeros
        return count; // Never returns -1 (end of stream)
    }
}

Or more realistically, maybe a stream that returns data from external hardware, which in certain cases might return lots of zeros (such as a game controller sitting on your desk). Either way we have an infinite loop. This particular non-terminating condition stands out, but sometimes they don't.

A completely real-world example as in an app I'm writing. An endless stream of zeros will be deserialized into infinite "empty" objects (until the collection class or GC throws an exception because I've exceeded two billion items). But this would be a completely unexpected circumstance (considering my data source).

How important is it to have absolutely no non-terminating conditions? How much does this affect "robustness?" Does it matter if they are only "theoretically" non-terminating (is it okay if an exception represents an implicit terminating condition)? Does it matter whether the app is commercial? If it is publicly distributed? Does it matter if the problematic code is in no way accessible through a public interface/API?

Edit: One of the primary concerns I have is unforseen logic errors that can create the non-terminating condition. If, as a rule, you ensure there are no non-terminating conditions, you can identify or handle these logic errors more gracefully, but is it worth it? And when? This is a concern orthogonal to trust.