I already had about 30 pages of graphs typeset with xymatrix for my thesis before discovering tikz; but was so impressed by it that I was happy to rewrite them all. As well as (imho) looking better, it gave me cross-platform compatibility - xypic seems to need pstricks, so on the mac with TeXshop (which uses pdflatex, I assume) the old graphs couldn't even be rendered.
Its ability to construct graphs iteratively can also be a massive timesaver- for instance, I wanted a bunch of otherwise identical rectangles at various positions, so with tikz could just loop over a list of their first coordinate rather than having to tediously cut,paste and modify an appropriate number of copies of the command for a rectangle. Particularly handy when I then decided they all needed to be slightly wider!
There's a gallery of tikz examples here, to give you some idea of what it's capable of (and with the relevant source code- I did find the manual a bit hard to understand and learnt mostly by examples or trial and error).
The vector graphics package inkscape (which I used to use for drawing more complicated graphs for inclusion as eps images) also apparently has a plugin to export as tikz, although I haven't tried that out.
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