Two papers I would include are:D. Kozen, Indexing of subrecursive classes, STOC, 1978.R. Ladner, On the Structure of Polynomial Time Reducibility, JACM, 1975.
What are the classic papers from the recursion theoretic area of complexity theory?
cc.complexity theory;lo.logic;computability;big list;structural complexity
Hajek, P. Arithmetical hierarchy and complexity of computation. Theoret. Comp. Sci. 8 (2): 227-237, 1979.  Started the study of the complexities of index sets (where their complexities often lie somewhere in the arithmetical hierarchy; see this answer to another question.)On the study of polynomial-time degrees (buzzword=polynomial-time degree theory, for the sake of future searches) I'd say these papers are of interest (several of them are based on Ladner's technique):Homer, S. Minimal degrees for polynomial reducibilities.  J. ACM 34(2):480-491, 1987.Schning, U. Minimal pairs for P. Theoret. Comp. Sci. 31: 41-48, 1984.Downey, R. Nondiamond theorems for polynomial time reducibility. Journal of Computer and System Sciences 45(3):385-195, 1992.Downey, R. and Fortnow, L. Uniformly hard languages. Theoret. Comp. Sci. 298(2): 303-315, 2003.Fenner, S., Homer, S., Prium, R. and Schaefer, M. Hyper-polynomial hierarchies and the polynomial jump. Theoret. Comp. Sci. 262: 241-256, 2001.Probably a forward and backwards reference search will find several more papers in the same area (though it's not that big an area!).