My best experience with TDD is centered around the pyftpdlib project. Most of the development is done by the original author, and I've made a few small contributions, but it's essentially a solo project. The test suite for the project is very thorough, and tests all the major features of the FTPd library. Before checking in changes or releasing a version, all tests are checked, and when a new feature is added, the test suite is always updated as well.
As a result of this approach, this is the only project I've ever worked on that didn't have showstopper bugs appear after a new release, have changes checked in that broke a major feature, etc. The code is very solid and I've been consistently impressed with how few bug reports have been opened during the life of the project. I (and the original author) attribute much of this success to the comprehensive test suite and the ability to test every major code path at will.
From a logical perspective, any code you write has to be tested, and without TDD then you'll be testing it yourself manually. On the flip side to pyftpdlib, the worst code by number of bugs and frequency of major issues, is code that is/was solely being tested by the developers and QA trying out new features manually. Things don't get tested because of time crunch or falling through the cracks. Old code paths are forgotten and even the oldest stable features end up breaking, major releases end up with important features non-functional. etc. Manual testing is critically important for verification and some randomization of testing, but based on my experiences I'd say that it's essential to have both manual testing and a carefully constructed unit test framework. Between the two approaches the gaps in coverage are smaller, and your likelihood of problems can only be reduced.