Apart from winning the Cold War (I know most liberals think he didn't), his most remarkable achievement was in turning around the disastrous economy which started under Richard "Wage-and-Price-Controls" Nixon, and got even worse under Jimmy "Malaise" Carter.
Under Carter, the prime interest rate was 21%, and inflation was in double digits. To live in an economy like that was pretty scary. Carter was completely unable to do anything to solve the problem, except to lecture Americans about the need to get out of their "malaise."
Reagan came in, implemented tax cuts, threw out price controls on energy, and after a brief recession which was the inevitable result of coming out of Carter's disastrous economy, started an economic boom that pretty much went through the Clinton years.
Reagan made free market economics respectable after decades of Keynesian idiocy.
He helped change the way we thought about ourselves. Carter was convinced, and tryed to convince us, that America`s greatness was over. Reagan thought that our greatness was just beganning. Once he did that, all the rest fell into place.
I disagree with Nixon's wage and price controls as well. But let's be reasonable about this. When Carter took over this nation was nowhere near as big a disaster as when he left. Carter was devoid of the skills to be President. He screwed up alliances, the economy, the military and even the self-confidence of our nation. Nixon had his problems, but I wouldn't mention his name in conjunction with Carter's inept administration. Carter did it all by himself.
Some say that Carter was screwed by oil price increases. I'm not convinced that was the problem. If people will note, oil prices shot up in the last few years also. Did interest rates hit 21%? No. And there goes Jimmy's claim. He was, is and always will be a bumbling fool.