Ideally, human efforts in testing should focus on building tests -- figuring out the strategies, test cases, and test data. From there, we'd rather let the computer run the tests and verify the results. If you had to test everything manually every day, you would either not do it, or really start to hate your job.
There are many kinds of automated tests. Sometimes the lines between the types blur a little, and sometimes the vocabulary varies, but I'd like to discuss two general kinds of automated tests: functional tests and unit tests. Each type of test has strengths and weaknesses, but together are complementary, rather than competitive in an automated testing strategy.
First some simple definitions:
Functional testing is sometimes also called integration testing, because it is all about making sure that the smaller parts work together correctly. In a layered architecture, a functional test may cover modules at a certain layer and below.
The single greatest strength of functional tests is that they test the software in the same environment that the software will ultimately be used in. They test what ultimately matters, and so are vitally important.
Functional tests do have shortcomings, though.
First, they require a working system to run. That is, the code has to be complete enough to hook the pieces together and do something in order to test it. This tends to push the functional tests into the later stages of development. Sometimes engineers give optimistic estimates for projects, and when the choice comes to ship or slip in order to add tests, the tests usually lose.
Some parts of the system are hard to test automatically in the context of the real system. The user interface, for example, can be particularly thorny (see the References, below, for more on this subject). As an extreme example, consider printing. The real system context means that ultimately you've got a piece of paper with some output on it. I can think of a potential way to test that output automatically (it involves one of those all-in-one devices that can print and scan, and some pattern matching software... and maybe a robot) but it starts to become impractical.
Functional tests also tend to require sophisticated configuration in order to run. Since they are testing the real system, they require real data. When I say "real data" in this case, I don't mean that it can't be contrived test data. I mean that if the system communicates with a database, there has to be a real database full of data down there.
Unit tests are a staple of software engineering. Steve McConnell, in Code Complete says, "Regardless of your integration or system-testing strategy, you should test each unit thoroughly before you combine it with any others." (p. 592)
Unit testing strategy encourages isolating the code being tested from the rest of the system. This typically means writing stubs that implement the same interface as the subsystems the main code will integrate with. It's important to realize that a stub provides a trivial implementation -- you're not rewriting all the functionality of the system to be stubbed out. At first thought, writing stubs seems counterproductive, but it actually provides some great benefits.
First, having the stub means you don't need the real thing to do your own programming. Instead of waiting for someone else to finish their piece, you can complete your unit that is dependent on it by coding to your stub. By taking advantage of the stub, you can write unit tests early in the development cycle, and find and fix defects earlier (and more inexpensively) than waiting for the integration test. The integration test will later flush out different interpretations of the interface between the stub and the real component.
Stubs might make some tests more practical as unit tests than as functional tests. The printer could be "stubbed out" such that the data sent there is easier to verify programmatically. This clearly isn't sufficient to say that printing is working correctly, but it can uncover a large class of bugs that would probably have required manual testing if we always sent paper out the printer.
Unit tests can take advantage of stubs to reduce configuration. Instead of requiring a real database, the test runs against the stub database, and the test code can communicate with the stub directly to know the "right answers" in advance. The stubbed version is also easier to get failures from in order to test error conditions. If the database has a problem when it runs out of disk space, you don't have to fill up the disk to test that condition -- the stub database just simulates the error.
In addition to lighter configuration, independence from the real system means that unit tests execute very quickly -- there isn't the latency of starting up the whole system. This quickness lets you run your unit tests very frequently -- even every time you compile. That moves defect discovery as early as possible in construction. If a test fails that was previously working, you've just broken something in whatever you did since your last compile.
If you write your unit tests very early (even before the code perhaps), then you're maximizing their usefulness. When writing code, we usually don't wait until integration to see if anything works. We usually try things out as we go. That's manual testing, and it takes time and effort. It makes the most sense to have the automated test from the start instead of adding them to test routines we've already tested and debugged manually.
It is easier to get complete coverage of code with unit tests, where you're able to be "up close" to the code. It's kind of like running wires through a wall: it's a whole lot easier when the studs are exposed rather than with the drywall, paint, and outlet covers in place.
Unit tests can reduce unpleasant surprises in some cases. If the system as a whole calls a unit in a particular way, a functional test might not catch some defects in the unit -- which is OK because the functionality isn't used. But if a new feature or bug fix changes the behavior, you might suddenly find a rat's nest of problems. If the unit has its own tests, though, you can be confident that changes in usage patterns will go smoothly.
Finally, an additional benefit of testing in isolation is that it can improve the design of the code itself. Kent Beck, one of the authors of the JUnit testing framework, has even argued that unit testing is an analysis and design technique, and not so much a testing technique. (See References). The design improvements tend to be in the area of reduced coupling (which is a huge focus of design generally), since it is hard to isolate a tightly coupled unit in order to test it in the first place, but it leads to other improvements as well.
One of unit testing's weaknesses is implied by the last strength. If existing code wasn't written with a fair amount of attention given to testing and decoupling, it can be very difficult to add unit testing later. For example, if instantiating an object requires most of the system to be present, you're going to have a hard time writing a unit test. A functional test may be the only choice.
Another weakness of unit tests is that stubs are not the same as the real system -- hence the need for functional tests to ensure that the system as a whole hangs together correctly.
In my opinion, the balance between effort spent creating functional versus unit tests should be tilted toward unit tests. Unit tests have a long list of benefits over functional tests, so focus on getting good coverage through them. Functional tests should then be used to test general cases to verify that the whole system hangs together.