Influential results by Swinnerton-Dyer The conjecture of Birch and Swinnerton-Dyer had a tremendous influence on the development of arithmetic geometry.  Which other results of Swinnerton-Dyer have had a lasting influence?
[edit, in answer to Yemon Choi] 
The influence of BSD has been multifold. There was the initial work to get an exact formula for the leading term and extend it to abelian varieties, which lead to progress on duality in Galois cohomology of number fields and integral models of abelian varieties.  It served as a prototype for general conjectures about special values of L-functions (Tate, Beilinson, Bloch-Kato).  The attempts to prove it have opened new fields of research (like the Gross-Zagier theorem that paved the way to Kudla's program, some kind of arithmetic mirror symmetry, or Coates-Wiles result that gave a boost to Iwasawa theory), etc. 
 A: Just to show the limited value of citation counts, the most cited paper of Sir Peter Swinnerton-Dyer on MathSciNet is not his 1965 paper with Birch, but a 1954 paper with Atkin on Some properties of partitions:

In their paper, Atkin and Swinnerton-Dyer proved the startling fact
  that for the three values $m = 5, 7, 11$ and every value of $r
= 0, 1, ... ,m -1$ the generating function $$\sum_{n\geq 0}p(mn+r)q^n,$$ with $p(n)$ the number of partitions of $n$, is
  congruent modulo $m$ to a simple infinite product.    

as discussed in:  Winquist and the Atkin-Swinnerton-Dyer partition congruences for modulus 11 
A: "The Hasse problem for rational surfaces" by Birch and Swinnerton-Dyer is certainly influential in the study of obstructions to the Hasse principal, as far as I understand there are examples of families surfaces for which the Hasse principal fails which are constructed here including an example for a del Pezzo surface to add to an example of Iskovskih. Given the interest in showing that for many families of surfaces the Brauer-Manin Obstruction fully accounts for obstructions to the Hasse-principal, having these counterexamples to the Hasse principal at hand is certainly important.
