Today we threw the big lever and turned on our new search backend at mediawiki.org.  It isn't the default yet but it is just about ready for you to try.  Here is what is we think we've improved:
1.  Templates are now expanded during search so:
1a.  You can search for text included in templates
1b.  You can search for categories included in templates
2.  The search engine is updated very quickly after articles change.
3.  A few funky things around intitle and incategory:
3a.  You can combine them with a regular query (incategory:kings peaceful)
3b.  You can use prefix searches with them (incategory:norma*)
3c.  You can use them everywhere in the query (roger incategory:normans)

What we think we've made worse and we're working on fixing:
1.  Because we're expanding templates some things that probably shouldn't be searched are being searched.  We've fixed a few of these issues but I wouldn't be surprised if more come up.  We opened Bug 53426 regarding audio tags.
2.  The relative weighting of matches is going to be different.  We're still fine tuning this and we'd appreciate any anecdotes describing search results that seem out of order.
3.  We don't currently index headings beyond the article title in any special way.  We'll be fixing that soon. (Bug 53481)
4.  Searching for file names or clusters of punctuation characters doesn't work as well as it used to.  It still works reasonably well if you surround your query in quotes but it isn't as good as it was.  (Bugs 53013 and 52948)
5.  "Did you mean" suggestions currently aren't highlighted at all and sometimes we'll suggest things that aren't actually better. (Bugs 52286 and 52860)
6.  incategory:"category with spaces" isn't working. (Bug 53415)

What we've changed that you probably don't care about:
1.  Updating search in bulk is much more slow then before.  This is the cost of expanding templates.
2.  Search is now backed by a horizontally scalable search backend that is being actively developed (Elasticsearch) so we're in a much better place to expand on the new solution as time goes on.

Neat stuff if you run your own MediaWiki:
CirrusSearch is much easier to install than our current search infrastructure. 

So what will you notice?  Nothing!  That is because while the new search backend (CirrusSearch) is indexing we've left the current search infrastructure as the default while we work on our list of bugs.  You can see the results from CirrusSearch by performing your search as normal and adding "&srbackend=CirrusSearch" to the url parameters.

If you notice any problems with CirrusSearch please file bugs directly for it:  https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=CirrusSearch

Nik Everett