Hello all,
The SPARQL endpoint we are running at http://query.wikidata.org has several measures in place in order to ensure it stays up and running and available for everyone, for example the 30 sec query timeout. This is necessary but also prevents some useful queries from being run. One way around this is Linked Data Fragments. It allows for some of the query computation to be done on the client-side instead of our server.
We have set this up now for testing and would appreciate your testing and feedback. You can find out more about Linked Data Fragments http://linkeddatafragments.org/concept/ and documentation for our installation https://www.mediawiki.org/wiki/Wikidata_query_service/User_Manual#Linked_Data_Fragments_endpoint. Also, you can see a demo of client-side SPARQL evaluation and LDF server usage here: http://ldfclient.wmflabs.org/
Please note - it's in no way a production service for anything, just a proof-of-concept deployment of LDF client. If you like how it works, you can get it from the source https://github.com/LinkedDataFragments/jQuery-Widget.js and deploy it on your own setup.
Feel free to ask Stas (Smalyshev (WMF)) for any further question!