In a fast paced smaller organization, I find that developers are so pressured to stay productive and move fast that they often simply don't bother to test their own changes.

We have a general policy that states that if you make a change (whether it is a bug fix or enhancement) the developer should test it him/herself before submitting the code for further QA.

We don't actually write unit tests for most instances because our screens are mostly designed in a way where if a change is made on the screen, the rest of the logic has to be traversed through in order to find out if the change was successful regardless.

I find it imperative that the developer does their own testing, whether it is documented or not, because they are the ones who best know where the potential weak points in the logic may be.

So I would say, even if you don't write unit tests for every little part of the system, common sense testing should be done regardless.