The goal of test automation should be to reduce the number of tests that need to be run manually, not to eliminate manual testing entirely. [Source]
The problem is that the goal of test automation should not be to reduce either test resources or cycle time. The goal should be to reduce the risk and cost of software failure by increasing test coverage. [Source]
Efficiency- This can be one Test Automation Goal, where the key aspects may be reducing testing costs, reducing the time in the testing phase, automating regression testing or improving test coverage. [Source]
Test automation should be measurable so that you can tell whether or not you have achieved it. Objectives should be realistic and achievable; otherwise, you will set yourself up for failure.
Objectives for test automation should support testing activities but should not be the same as the objectives for testing. Testing and automation are different and distinct activities. [Source: That's No Reason to Automate, by Dorothy Graham, Mark Fewster]
Following are also examples of possible goals:
Speed up testing to allow for accelerated releases
Allow testing to occur more frequently
Improve test coverage
Ensure consistency
Improve the reliability of testing
Define the testing process
[Source]