1. He was influential. He influenced students through his textbook, and he influenced the entire economics profession through his dissertation, published as "Foundations of Economic Analysis." Readers of this blog will tend to disapprove of his influence, in that it promoted Keynes and the use of mathematical modeling. Perhaps Milton Friedman was more influential on policy. But Samuelson was more influential on the internal dynamics of the economics profession. On that score, I would say that he was without peer in this century
2. Compared with later generations of economists, he was more nuanced in his thinking and not as capable a mathematician. When I was an undergraduate, Bernie Saffran liked to repeat the joke that Samuelson had never proven a true theorem, meaning that his proofs typically had to be corrected.
3. He taught me Austrian capital theory. I had him for a half-semester course on capital theory, and what I remember best was his description of the Austrian model of roundabout production. That was the only Austrian economics I encountered until quite recently.
As to the techniques I learned from him and used: comparative statics of constrained optimization, the correspondence principle and the envelope theorem, factor price equalization in international trade, valuation of real options, the list could go on.
The list could certainly include Samuelson's proof that stock prices follow a random walk, as Tyler Cowen notes.
For a recent interview that demonstrates the nuanced Samuelson, see The Atlantic. For example, in part two of the interview, he advocates teaching economic history.
John Maynard Keynes may have had more influence on policy makers, Milton Friedman on citizens, Kenneth Arrow on economic theory, but Samuelson had more influence on the way economics is done today, and the purposes to which it is put, than any other economist of the twentieth century.