This question gets asked a lot, particularly as there is a cost in implementing automated tests. There is also a benefit, but it is harder to quantify. When a development team has a limited amount of time between releases there is often a preference to implement new functionality rather than automate testing for existing functionality. With Agile Software Development methodologies, the role of the tester is more complex, but automation of testing is clearly a responsibility.
It is easy to say that 100% of the system functionality should be tested automatically and to ensure that regressions do not occur, that this testing should be performed by a developer before they check in changes. It is hard to justify the cost of doing so as the information on how many defects automated testing prevented does not often get recorded.
The simplest place to start is to review the regression defects that have been raised in the past. This should highlight the functionality that tends to break the most when changes are made. After implementing automated regression testing the journey starts in growing the range of automated test suites. Assuming, of course, that developers are using the automated testing before checking in their changes, one should also see a reduction of the regression defects being raised in areas with automated testing.