In my work (writing scientific software in C++), I often get asked by the people who use the software to get their work done to add some functionality or change the way things are done and organized right now. Most of the time this is just a matter of adding a new class or a function and applying some glue to do the job, but from time to time, a seemingly simple change turns out to have far-reaching consequences that require me to redesign a substantial amount of existing code, which takes a lot of time and effort, and is difficult to evaluate in terms of time required. I don't think it has as much to do with inter-dependence of modules, as with changing requirements (admittedly, on a smaller scale).
To provide an example, I was thinking about the recently-added multi-user functionality in Android. I don't know whether they planned to introduce it from the very beginning, but assuming they didn't, it seems hard to predict all the areas that will be affected by the change (apps preferences, themes, need to store account info somehow, etc...?), even though the concept seems simple enough, and the code is well-organized.
How do you deal with such situations? Do you just jump in to code and then sort out the cruft later like I do? Or do you do a detailed analysis beforehand of what will be affected, what needs to be updated and how, and what has to be rewritten? If so, what tools (if any) and approaches do you use?