EDIT: I now think that this list is long enough that I shall be maintaining it over time--updating it whenever I use a new book/learn a new subject. While every suggestion below should be taken with a grain of salt--I will say that I spend a huge amount of time sifting through books to find the ones that conform best to my (and hopefully your!) learning style.
Here is my two cents (for whatever that's worth). I tried to include all the topics I could imagine you could want to know at this point. I hope I picked the right level of difficult. Feel absolutely free to ask my specific opinion about any book.
Basic Analysis: Rudin--Apostol
Measure Theory: Royden (only if you get the newest fourth edition)--Folland
General Algebra: D&F--Rotman--Lang--Grillet
Finite Group Theory: Isaacs-- Kurzweil
General Group Theory: Robinson--Rotman
Ring Theory: T.Y. Lam-- times two
Commutative Algebra: Eisenbud--A&M--Reid
Homological Algebra: Weibel--Rotman--Vermani
Category Theory: Mac Lane--Adamek et. al--Berrick et. al--Awodey--Mitchell
Linear Algebra: Roman--Hoffman and Kunze--Golan
Field Theory: Morandi--Roman
Complex Analysis: Ahlfors--Cartan--Freitag
Riemann Surfaces: Varolin(great first read, can be a little sloppy though)--Freitag(overall great book for a second course in complex analysis!)--Forster(a little more old school, and with a slightly more algebraic bend then a differential geometric one)--Donaldson
SCV: Gunning et. al--Ebeling
Point-set Topology: Munkres--Steen et. al--Kelley
Differential Topology: Pollack et. al--Milnor--Lee
Algebraic Topology: Bredon--May-- Bott and Tu (great, great book)--Rotman--Massey--Tom Dieck
Differential Geometry: Do Carmo--Spivak--Jost--Lee
Representation Theory of Finite Groups: Serre--Steinberg--Liebeck--Isaacs
General Representation Theory: Fulton and Harris--Humphreys--Hall
Representation Theory of Compact Groups: Tom Dieck et. al--Sepanski
(Linear) Algebraic Groups: Springer--Humphreys
"Elementary" Number Theory: Niven et. al--Ireland et. al
Algebraic Number Theory: Ash--Lorenzini--Neukirch--Marcus--Washington
Modular Forms: Diamond and Shurman--Stein
- Lorenz and Levy--Read chapters 23,24,25. This is by far my favorite quick reference, as well as "learning text" for the basics of local fields one needs to break into other topics (e.g. class field theory).
- Serre--This is the classic book. It is definitely low on the readability side, especially notationally. It also has a tendency to consider things in more generality than is needed at a first go. This isn't bad, but is not good if you're trying to "brush up" or quickly learn local fields for another subject.
- Fesenko et. al--A balance between 1. and 2. Definitely more readable than 2., but more comprehensive than 1. If you are wondering whether or not so-and-so needs Henselian, this is the place I'd check.
- Iwasawa--A great place to learn the bare-bones of what one might need to learn class field theory. I am referencing, in particular, the first three chapters. If you are dead-set on JUST learning what you need to, this is a pretty good reference, but if you're likely to wonder about why so-and-so theorem is true, or get a broader understanding of the basics of local fields, I recommend 1.
Class Field Theory:
- Lorenz and Levy--Read chapters 28-32, second only to Iwasawa, but with a different flavor (cohomological vs. formal group laws)
- Tate and Artin--The classic book. A little less readable then any of the alternatives here.
- Childress--Focused mostly on the global theory opposed to the local. Actually deduces local at the end as a result of global. Thus, very old school.
- Iwasawa (read the rest of it!)
- Milne--Where I first started learning it. Very good, but definitely roughly hewn. A lot of details are left out, and he sometimes forgets to tell you where you are going.
Metric Groups: Markley
Algebraic Geometry: Reid--Shafarevich--Hartshorne--Griffiths and Harris--Mumford