Tim Thompson, Spaceman Spiff and antoniseb all gave great answers. I just want to add a few more notes.
As they all said, or implied, redshift quantization disappears when a uniform survey is carried out. There are many reasons why we are more likely to find a quasar at one redshift than another, and early catalogs did not necessarily take these into account or had too small a sample size to make any statistical statements. Creating a uniform quasar sample is no easy task, but it is absolutely necessary, if you want to perform any statistical tests.
Look at Figure 3 in the SDSS Data Release 5 Quasar paper (page 24, described at the top of page 12):
http://arxiv.org/abs/0704.0806
It shows the redshift distribution of quasars in the latest-but-one SDSS quasar catalog (the DR6 catalog hasn't been completed yet). The dashed histogram is the redshift distribution after *known* selection effects have been accounted for. Notice how any apparent structure goes away? Quoting from the second paragraph of page 12:
Quote:
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Repeating the analysis of Richards et al. (2006) for the DR5 sample reveals no structure in the redshift distribution after selection effects have been included (see lower histogram in Figure 3); this is in contrast to the reported redshift structure found in the SDSS quasar survey by Bell & McDiarmid (2006). ... Accounting for selection effects significantly reduces the number of objects as compared with the raw, more heterogeneous catalog, but the smaller, more homogeneous sample is what should be used for statistical analyses.
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In Bell & McDiarmid, they did not pay attention to any of these selection effects. But they are the *most* important contributor to the apparent structure in that plot. And they are well understood; a large part of the work that went into designing the SDSS quasar survey involved modelling and accounting for this selection function.
I'd guess that there are probably fewer than 20 (maybe even 10) active astronomers who still think redshift quantization---of any form---is viable or even worth bothering with. If someone can correct me on that, I'd love to hear it!
Hope this was helpful. As I said, the others did a great job above, though I really don't like think the wikipedia page is very balanced on this subject.