Matthew Emerton mentioned recently the relevance of Dwork's "p-adic cycles". As I wonder if I should read that, reviews of it are ambiguous, I'd be happy on remarks and possible further bibl. hints. And I'd enjoy hints where one finds surveys etc. related to Mazur's "Theme of p-adic variation" and how that develops.
You could read Mazur's article in the $p$-adic monodromy volume. And also Katz's Travaux de Dwork, as well as his two articles on Serre--Tate theory (LNM 828?), and the accompanying article of Deligne and Illusie on K3 surfaces. You could also read Gross's Tameness Criterion paper in Duke from the late 80s, which uses Dwork's ideas and related $p$-adic techniques. And there is Nygaard's article on the Tate conjecture for K3's over finite fields.
Dwork is difficult, and I don't recommend reading him in a vacuum or for casual entertainment. But his ideas and insights are very deep, and very original. (His actual techniques are very involved, and I am not sure that I would recommend learning them before you learned some more standard ideas from $p$-adic geometry, such as are explained in the above references.)