From my experience unit tests are incredibly useful when developing code that is perfectly suited for unit tests, generally things that have predictable inputs and outputs, and don't have dependencies or global effects. On the other hand if you're testing boilerplate code with a lot of complex dependencies (i.e. an MVC controller) it's probably better to cover it with integration or acceptance tests.
You should move as much code as reasonably possible into unit-testable blocks, but going out of your way for 100% unit-test coverage leads to tests that aren't worth writing and updating.
Then there are tricks, like mocking outside services (so that you don't have to actually hit remote services when running acceptance tests) and comparision testing, i.e. not testing the contents of an XML document but just storing it and comparing output directly to it. When testing APIs I also automatically test inputs and outputs on endpoints against a specification, which is a pretty good way of testing both the endpoints and the specification.
I also think that unit tests are a great way to force yourself to write easily testable code, which is usually better structured than non-testable code :)
But in general code needs to be tested if you care about it working. Any endpoint you don't test will eventually be broken.
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