While there is no hard-and-fast minimum ACT score that guarantees college acceptance, the chart available at the link below (see Additional Resources) details the average scores for some of America's top public universities.
For instance, those attending UCLA who scored a 24 on the ACT rank in the 25th percentile for the school, while those in the 75th percentile averaged a 30. Other composite scores in the 25th percentile at top public universities include 27 (College of William & Mary, Georgia Tech, and Michigan), 23 (California-San Diego and UC-San Diego), and 25 (North Carolina-Chapel Hill).
Meanwhile, average composite scores in the 75th percentile at these top public universities range from 32 (William & Mary) to 29 (UC-San Diego).
The average composite scores for some of America's top colleges range slightly higher than their public counterparts. For instance, the average composite scores in the 75th percentile for ten of America's top colleges range from 32-34, while those in the 25th percentile range in scores from 27-29.
College Apps (first link under References) presents several schools nationwide that require neither an SAT nor an ACT score to be granted admission for in-state residents. Among the major names on the list are the University of Texas at Austin, Arizona State University, and Kansas State University. However, be advised to visit each school's rule book, as some of these do require SAT/ACT scores from out-of-state applicants.
For those interested in seeing how you stack up against your fellow ACT-takers, this link (see the second link under Additional Resources) provides average scores from 2008, sorted nationally or by region. While this won't necessarily guarantee you admission to your college of choice, it will help you see how you measure up against others who have recently taken the test.
For more information on the ACT, including some history and specifics of the test, please visit the ACT home page.