Automated Regression Testing
Can an agile team succeed with no test automation? Maybe, but the successful teams that we know rely on automated regression tests. If you are spending all your time doing manual regression testing, you will never have time for the important exploratory testing that will ferret out the damaging behaviors lurking in the code.
Agile development uses tests to guide development. In order to write code to make a test pass, you need a quick and easy way to run the test. Without the short feedback cycle and safety net regression that suites provide, your team will soon become mired in technical debt, with a growing defect queue and ever-slowing velocity.
Test Automation is a team effort
Test Automation is a team effort. It's also hard, at least at first. There's often a big "hump of pain" to overcome. If you manage a development or testing team, make sure you are providing support in the form of time, training, and motivation. If you are a tester on a team with no automation, and the programmers are too frantic trying to write production code to stop and think about testing, you have a big challenge ahead of you.
Experiment with different ways of getting support from management and from team members to start some tiny automation effort.