Early on in my career I used to think that there existed code that was "too complicated" to unit test, especially code doing multithreading. A few years experience on this type of code base taught me that "too complicated to unit test" is just another way of saying "unmaintainable". What I really needed to do was to change the idioms I was using so I could write something unit testable .
The flip side to that mistake was I argued that since we couldn't unit test the most complicated parts, we shouldn't unit test the simple code either. The mistake here was the assumption was that bugs were much more likely to appear in the complex code then the simple code. Whereas in reality, because the complex code was complex, it was subject to a lot more ad hoc and integration testing than the simple code, which just "obviously" worked. The key thing is that most bugs turn out to be trivial (e.g. cutting and pasting a loop and not changing the loop variables in all cases), but code is so dense with information it is often very hard to spot these mistakes by eye, so with their path untested they all too easily make it to production and cause some behavioral bug in some edge case, and after days go by before it is observed, then you have spent hours tracking it down to a one-line bug, you will wonder how the entire software world keeps itself together.
That being said, you have to be careful with unit tests. They can add a lot of almost deadweight code to your base, making trivial changes to functionality take several hours just in refactoring unit tests. Now, modern IDEs with refactoring tools can help a lot here . But certain of these problems are not refactorable.
The most important thing is not to treat test code as a second class citizen. In terms of quality it must be treated the same as production code So for example, since we all know that copying and pasting a code block 10 times is bad in production code, then it is just as bad, for all the same reasons, in a test, or across a set of tests. What this means in practice is you end up with lots of little methods to construct helper objects to put into tests, e.g. replacing N replicas of this:
MyObjectUnderTest obj = new MyObjectUnderTest();
With N of this:
doTest(createObjectUnderTest("foo", "bar", "baz"));
A second important aspect is to test just 1 object at a time - don't couple objects under test. Doing 2 (or more) at once often seems like a time saver ("I'm testing three objects with one test, yay productivity!"), but as soon as you want to refactor one of the objects (e.g. to use it in another place) you will be regretting your choice as you have to understand the complex interactions the test was testing, and then rewrite them. Mocking frameworks and judicious use of Abstract Classes/Interfaces can be your friend here.
As to when to write the tests, TDD is fine if it works for you. I find it most useful when trying to write classes where I want to get the API right. But after all I am generally writing a applications as opposed to a library, and so any individual class's interface is not that important, and so I use it rarely.
One thing I do force myself to do is write code in units, and write the test straight after each unit. The thing I noticed is that if I delay writing unit tests until after all the units are working together end to end, then because after all the system "already works" my subconscious enthusiasm for writing unit tests falls markedly, and their quality and coverage fall likewise. Whereas if I write the unit tests just after each unit, it's part of "getting everything to work", and so I am willing to put the effort into doing it well.
In the end though, I have found the greatest value of unit tests is that they give me direct feedback as to just how high my error rate is in writing code. I have lost count of how many times I have written the code, written the test, thought "this is sure to work", and in fact had several quite serious bugs that need to be fixed. It is forever a humbling experience, but humility is a good value to have when working on large, complex software systems in a corporate "we need it yesterday" environment.
 In particular, I was writing mulithreaded stuff on the Win32 API and trying to get by with Semaphores and Events, and interlocked stuff for cross thread synchronization. All very difficult to unit test. When I finally switched to Posix Condition Variables, everything was much easier. The other thing I learned here was as much as possible objects should not own threads - rather they should be driven by threads. Thus you just need to unit test state transitions of method calls. Now, this is still not checking for race conditions and deadlocks - for that the only solution I have found is good up front design with well defined semantics.
 It's one of the many reasons that dinosaurs still using Emacs for writing Java are doing a bad job - they either aren't writing enough unit tests or not doing enough refactoring.
 Of course a better language with named parameters would make this all less monotonous. But like most people in the real world I am stuck with Java or C++ on any project large enough that it needs type safety.