TITLE: What is the Zariski topology good/bad for? 
QUESTION [34 upvotes]: In a comment to this question the quotation "The Zariski Topology is the 'Wrong' topology for Algebraic Geometry" appears.
Well, so some spontaneous questions arise: 
1) What is Zariski topology good for in algebraic geometry? In other words, what can you do with it, without referring directly to some finer Grothendieck topologies?
2) On the other hand, which concepts which are analogs of concepts in -say- analytic geometry or topology, really need finer Grothendieck topologies to be generalized to the algebro geometric setting?
I think one could mention vector bundles for the 1), and principal bundles and projective bundles for 2). And also cohomology for 2), since it seems that the étale topology is best suited for reproducing a cohomology that resembles the singular one in the analytic setting. And also sheaf cohomology for 1).

Edit: I think it would also be nice if in the answers there were some brief comments about the sufficiency (or not) of Zariski topology to capture the essential geometric picture borrowed from analytic geometry and/or topology about (some of) the following contexts:

Patching of morphisms
Inverse function theorem & implicit function theorem
Existence of tubular neighbourhoods (?)
Local reducubility vs. global reducibility (analytic branches of a variety at a point..)
"Infinitesimal" properties given by the local ring at a point (Zariski vs. Hensel)
Vector bundles
Coherent sheaves (and patching thereof...)
Principal bundles (local triviality...)
Projective bundles (as above...)
In general, "locally trivial" fiber bundles (isotriviality vs. triviality...) 
Sheaf cohomology with constant coefficients vs. of coherent sheaves
Cech cohomology (as above...)
Covering spaces and fundamental group
Extracting topological/homotopical information via coverings
(any other topic you find interesting)

REPLY [2 votes]: algebraic geometry is not my field at all, but it seems like this is a bit of an answer, and i don't really know the details but maybe someone can fill them in. The Zariski topology is not good for doing homotopy theory. I have heard this at many seminars, specifically from someone who does motivic homotopy theory. So from that perspective it is not the right topology, but i can only say that i have heard this not that i understand why the Zariski topology is bad. I guess just naively it seems like it would be pretty hard doing homotopy theory on "any" line where your only open sets are finite complements.