A vexing part of algebraic topology is the lack of advanced textbooks - we have to make do with papers. The following is a list of my favorite papers and books. It is far from complete at this point.

After a first course

Mosher and Tangora

Milnor and Stasheff

Spectra

Much of this material uses the model category material

Diagram Spectra
Mandell, M A, J P May, S Schwede, and B Shipley. 2001. “Model Categories of Diagram Spectra.” Proceedings of the London Mathematical Society 82 (02): 441–512.

Model Categories

A good introduction is
Dwyer and Spalinski
A nice more advanced source is Hirschorn's text.
Finally, appendix of A of Higher Topos theory by Lurie is quite readable.

Abstract Homotopy Theory

Vogt - Homotopy Colimits
Vogt, R M. 1973. “Homotopy Limits and Colimits.” Mathematische Zeitschrift 134 (1): 11–52. This paper basically proves everything you want about homotopy colimits, and it does it cleanly. Even provides a proof of one of Thomason's results

Dwyer-Kan Simplicial Localization
Dwyer, W G, and D M Kan. 1980. “Simplicial Localizations of Categories.” J. Pure Appl. Algebra 17 (3): 267–284.
Dwyer, W G, and D M Kan. 1980. “Calculating Simplicial Localizations.” J. Pure Appl. Algebra 18 (1): 17–35.
Dwyer, W G, and D M Kan. 1980. “Function Complexes in Homotopical Algebra.” Topology 19 (4): 427–440.

K-theory and THH

The first things one should probably read are
Quillen, D. 1973. “Higher Algebraic K-Theory: I.” Higher K-Theories: 85–147.
and
Waldhausen, F. 1985. “Algebraic K-Theory of Spaces.” Algebraic & Geometric Topology LMN 1126: 318–419