There's also my own http://websolr.com/ running Apache Solr. Some other Solr services are mentioned elsewhere on the page.
I've also recently launched http://bonsai.io/ for a hosted ElasticSearch service. Because ElasticSearch is actually quite awesome (and I'm happy to answer questions about why).
For Sphinx, there's Flying Sphinx (by Pat Allen of Thinking Sphinx Ruby client fame, great guy), and IndexDen (which is Sphinx, not IndexTank).
There's a lot to be said for ElasticSearch's data distribution. It does sharding and replication really well. That makes my life easier, as a service provider, as well as the life of anyone that has to manage and scale an ES cluster. Or who doesn't want to have to deal with client-side sharding or worry about how many servers can crash before their search goes down.
ElasticSearch has very little ceremony around creating a new index and getting started with using it. You will eventually need to do some configuration to tune its behavior for your specific application, but the learning curve is nice and gradual. This makes ES great for exploration.
The JSON document store aspect of ElasticSearch is indeed very nice. The RESTful API is simple enough that you don't really need a client, just grab your favorite HTTP client library and start integrating. Plus, coupled with solid distribution, you're looking at a pretty viable standalone data store, IMO.
Also, very good documentation. And its user/developer community is all full of the really smart, enthusiastic early-adopter types right now :)
Not least, Lucene itself is hands down the last word when it comes to search.
There's also my own http://websolr.com/ running Apache Solr. Some other Solr services are mentioned elsewhere on the page.
I've also recently launched http://bonsai.io/ for a hosted ElasticSearch service. Because ElasticSearch is actually quite awesome (and I'm happy to answer questions about why).
For Sphinx, there's Flying Sphinx (by Pat Allen of Thinking Sphinx Ruby client fame, great guy), and IndexDen (which is Sphinx, not IndexTank).