An important aspect of testing is ensuring that your tests are run regularly and often. If you're following the test-driven development philosophy, you should be writing your tests before writing code and adapting your tests as new code is added. While this will give you a good idea of what is working and what isn't, it can be extremely time-consuming, and it doesn't cover cases where team members make changes but either don't write tests or don't run them before committing and pushing them to your DCVS repository.
The best way to ensure that your tests are run after every change is to use a third-party service, such as Travis CI. A tool such as Travis CI will add a webbook to your repository, and after every commit, it can be configured to run all your tests and notify you if and when your tests ever start failing.
Tip
In general, you should always verify that your code runs and that your tests pass before committing it to your repository.
Using Travis CI as an example...