Wiki Database, is there one?

It's not quite what you're looking for, but Semantic Mediawiki adds database-like features to MediaWiki:

http://semantic-mediawiki.org/wiki/Semantic_MediaWiki

It's still fundamentally a Wiki, but you can add semantic tags to pages ([[foo::bar]] [[baz::1000]]) and then do database-type queries across them: SELECT baz FROM pages WHERE foo=bar would be {{#ask: [[foo::bar]] | ?baz}}. There is even an embryonic SPARQL implementation for pseudo-SQL queries.

This might be like what you're looking for: dbpedia.org. They're working on extracting data from Wikipedia, and encoding it in a structured format using RDF, so that it can be queried using SPARQL.

Linkeddata.org has a big list of RDF data sets.

Something that might come close to your requirements is Google Docs.

What's offered is document editing roughly similar to MS Word, and spreadsheets roughly similar to Excel. I'm thinking of the latter, of course.

In Google Docs, You can create spreadsheets for free; being spreadsheets, they naturally have a row-and-column structure similar to a database, and which you can define flexibly. You can also share these sheets with other people. This seems to be a by-invite-only process rather than open-to-all, but there may be other possibilities I'm not aware of, or that level of sharing might be enough for you in any case.

OK this question is old, but Google led me here, so for anyone else out there looking for a wiki for structured data: Take a look at Foswiki.