"Non relational databases" have seen quite a bit of interest recently. There was a NOSQL meeting in San Francisco last week and they have very kindly put some slides and videos up. I find it interesting but haven't got enough data yet...
A couple of years ago, I heard someone talk about the possibility of eliminating "perlmod" as an obsolete technology. Fortunately, he could be assured that there was no "perlmod" deployed in his organization, so his objective was achieved.
Similarly, very, very few people use relational databases. Oracle, PostgreSQL and MySQL are all examples of databases which people call relational, but are not. Just today I wrote an SQL query which, as is so common, returned many duplicate results, something which does not happen in the relational model. While I can certainly sympathize with those who are fed up with the problems associated with our current crop of popular databases, I really wish they wouldn't get confused and suggest that the relational model is at fault.
I don't mean lump you with that group, by the way
Some background: Open Source Relational Databases.