I've admitted on a few occasions that I've never written a unit test for anything. This is something I keep meaning to change, if only I could find the time. For the time being, I can still keep the code dependencies and side-effects in my head so it has yet to cause any serious issues. I still slap my own hand, though.
There is, of course, a middle way. Implement as much testing as makes sense for you. Think Pareto.. just the right 20% of testing could give you 80% of the gains.
So.. implement integration tests that test your apps very broadly and as soon as one fails, you know you can start looking deeper. No need to always start with line by line unit tests :)