What are the classic papers from the recursion theoretic area of complexity theory?
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.
Schöning, 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!).