Most Agile approaches suggest Test-Driven-Development, but at least you should practice some form of technical excellence to satisfy the following Agile principles:
Continuous attention to technical excellence and good design enhances
Personally, I like the LeSS approach to technical excellence. A broad combination of quality practices.
Now in Agile teams, the question is not do we write tests or not, but who writes the test-cases. Developer should write test-cases, but testers could, product people could, anyone on the team could. Preferably the teams automate them aswell.
If your team does not have a nice balance of tests (unit, integration, and or end-2-end tests) then they are taking serious shortcuts and are cowboy coding in my book. With a high risk of very slow development in the long run, as:
Organizational Agility is constrained by Technical Agility
All Agile leaders suggest forms of testing in their writings, but I like those of Robert C. Martin the most. Be sure to read his Clean Code series starting with Clean Code: A Handbook of Agile Software Craftsmanship. Clean coders make tests period.
You are not Agile with just the process alone, I think we should talk more about the technical practices. An adaptable process is worthless if your product is not adaptable. Agile coding is all about refactoring and having a soft product that does not resist change. Testing is a strong part of this.