EDIT: Since this question is already bumped up, I will take this opportunity to make a longer list.
There are of course some classic references which are still very useful (I find myself having to look in them quite often despite the new sources available): Bourbaki, EGA IV, Serre's "Local Algebras" (very nice read and culminated in the beautiful Serre intersection formula).
There has been some work done in commutative algebra since the 60s, so here is a more up-to-date list of reference for some currently active topics (Disclaimer: I am not an expert in any of these, the list was formed by randomly looking at my bookself, and put in alphabetical order (-:). This is community-wiki, so feel free to add or edit or suggest things you found missing.
Cohen-Macaulay modules, from a representation theory perspective: Yoshino is excellent. Another one is being written.
Combinatorial commutative algebra: Miller-Sturmfels.
Free resolutions (over non-regular rings): Avramov lecture note
Geometry of syzygies: Eisenbud, shorter but free version here.
Homological conjectures: Hochster, Roberts (more connections to intersection theory), Hochster notes.
Integral closures: Huneke-Swanson, which is available free at the link.
Intersection theory done in a purely algebraic way: Flenner-O'Carrol-Vogel (for a very interesting story about this, see Eisenbud beautiful reminiscences, especially page 4)
Local Cohomology: Brodmann-Sharp, Huneke's lecture note (very easy to read), 24 hours of local cohomology (I have been told that this one was a pain to write, which is probably a good sign).
Tight closure and characteristic $p$ method: Huneke, Karen Smith's lecture note (more geometric, number 24 here), and of course many well-written introductions available on Hochster website.
