Which of Quillen's Papers Should I read? I just heard that Daniel Quillen passed on.  I am not familiar with his work
and want to celebrate his life by reading some of his papers.  Which one(s?)
should I read?
I am an algebraic geometer who is comfortable with cohomological methods in his field, but knows almost nothing about homotopy theory.  My goal is to gain a better appreciation of Quillen's work, 
not to advance my own research.
Here I tagged this question as "at.algebraic-topology, algebraic-k-theory" because I think these are the main fields in which Quillen worked.  Please add or change this if other tags are appropriate.
 A: I would definitely suggest his two-part paper, The Spectrum of an Equivariant Cohomology Ring.
He develops a ton of information concerning $H_G^*(X)$, and forms the basis for much of its use in future papers.
In terms of studying group cohomology, you should also check out his short paper Cohomology of Finite Groups and Elementary Abelian Subgroups (by Quillen and Venkov) which establishes the celebrated result:  If $u\in H^*(G,\mathbb{Z}_p)$ restricts to zero on every elementary abelian $p$-subgroup of $G$ (a finite group), then $u$ is nilpotent.  This paper is not even two pages long, although his original proof was contained in a different paper ("A Cohomological Criterion for p-Nilpotence").
A: Being a mathematical physicist, I have a particular fondness for his papers in Topology in the 1980s, alone or with Mathai, on the subject of superconnections:


*

*Superconnections and the Chern character, Topology 24 (1985) 89-95

*Superconnections, Thom classes, and equivariant differential forms, Topology 25 (1986) 85-100

*Superconnection character forms and the Cayley transform, Topology 27 (1988) 211-238
All are sadly hidden behind an Elsevier paywall...
A: Can I be the first to recommend Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 1971 29–56 (1971).
From the MR review: "In this important and elegant paper the author gives new elementary proofs of the structure theorems for the unoriented cobordism ring $N^\ast$ and the complex cobordism ring $U^\ast$, together with new results and methods. Everyone working in cobordism theory should read this paper."
The paper was revolutionary in (at least) two ways.


*

*The proofs are almost entirely geometric, with cobordism classes represented by proper oriented maps of manifolds. Quillen cites Grothendieck as inspiration for this, and such methods should appeal to algebraic geometers familiar with the Chow ring.

*Formal group methods are used to prove results in stable homotopy theory. It's hard to overestimate the impact this has had. Indeed almost all of the modern connections between homotopy theory and algebraic geometry seem to go through formal groups, drawing influence from Quillen's idea. 

A: Perhaps as an algebraic geometer, you might read his paper:On the (co-)homology of commutative rings , in Proc. Symp. on Categorical Algebra , (1970), 65–87, American Math. Soc.
This is fairly short and yet is one of the key papers in the area. It introduces ideas of homotopical algebra, which have been crucial in algebraic topology and algebraic geometry, yet the paper does not need a whole load of prior knowledge. The lecture notes on homotopical algebra and the paper on rational homotopy theory are beautiful in their use of techniques from adjacent areas to solve hard general problems and follow on from that initial work.
The algebraic K-theory papers are another thread, but these have been mentioned above.
A: Quillen's book on Homotopical Algebra is a great pleasure to read, and likely to appeal to a geometer.
A: There are a number of papers that I have affection for.  Those which I don't see listed:
"On the group completion of a simplicial monoid."  Before I read this paper I never really understood the appearance of the plus-construction.  This essentially proves the +=Q theorem.  (A little harder to find: Appendix Q in Friedlander-Mazur's "Filtrations on the homology of algebraic varieties.")
"On the formal group laws of unoriented and complex cobordism theory."  A very influential paper, along the likes that Mark Grant mentioned, and one which we've been trying to unravel the consequences of ever since.   (Bull. Amer. Math. Soc. 75 1969, 1293–1298.)
"The Adams conjecture."  Quillen's proof of the Adams conjecture by making use of a Brauer lift is short but wonderful.  (Topology 10 1971 67–80.)
