I am likely to get lynched for my opinion on this, but here I go.
While I have had this hammered into me over years of reading idealistic articles and sitting through far too many seminars and lectures categorically stating the nirvana like benefits of this, I too had similar questions in my mind. This line of thought can lead to massive over-engineering of the code, adding many man hours or more to design, development and testing estimates, increasing cost and overheads, when in reality this is not often the case. How many times have you actually reused your code or a library. If it is going to be used in many places, through numerous projects, then yes you should.
However, most of the time this is not the case. You will often find it more economical (in time and money) to only refactor your code for reuse and configurability when you actually know that you are going to use it again. The rest of the time the real benefits are lost.
This is not, I repeat NOT, an excuse to write sloppy, poorly designed, poorly documented code. This should be a fundamental that is so wholly ingrained in you that you could not break it, but writing a class for reuse is a waste most of the time as it will never get reused.
There are obvious exceptions to this. If you are writing third party libraries then obviously this is not the case and reuse and expansion should be key to your design. Certain other types of code should be obvious for reuse (Logging, Configuration etc.)
I asked a similar question here Code Reusability: Is it worth it It might help.
yagni.
http://en.wikipedia.org/wiki/YAGNI (*inserted by friendly editor :-) *)
fix the bugs in that horrenous code you're writing today.
refactor when the time comes.
If you work in a refactoring-friendly lanuguage I'd say NO. (In other languages I'm not sure)
You should make your code as loosley coupled as possible and keep things as simple as possible. Stay specific and dont generalize to unknown use cases.
This will make your code base prepared for the things the future will bring.
(And frankly, most anticipations of the future tend to be sufficiently off-mark not to warrant coding for it today)
Edit: It also depends on what you're doing. Designing apis for external users is not the same as developing a web app for your company