Transitive properties have wide use in Wikidata. Examples include basic membership properties like instance of (P31), subclass of (P279) and part of (P361); and genealogical properties like mother and father. The P31 and P279 properties are based on W3C recommendations for representing information in the Semantic Web -- rdf:type and rdfs:subClassOf.
The ability to draw conclusions from transitive properties is possible with RDFS query inference engines that implement SPARQL. A list of SPARQL implementations is available at http://www.w3.org/wiki/SparqlImplementations. Handling the simple entailments implied by P31 and P279 seems to be a core feature of querying in the Semantic Web.
http://meta.wikimedia.org/wiki/Wikidata/Technical_proposal#Optional_extensions_to_phase_3 mentions the first optional goal as "Develop and prepare a SPARQL endpoint to the data". While support for transitive properties presumably (and understandably) would not be part of Wikidata's initial support for SPARQL, a bit down the line it would be very helpful to have support for general transitive properties in Wikidata SPARQL queries, or at least the more limited and core feature of handling inferred claims for the rdf:type and rdfs:subClassOf (P31 and P279) properties.
Magnus Manske has also inquired about support for this kind of feature in http://meta.wikimedia.org/wiki/Talk:Wikidata/Development/Queries. An earlier version of this feature request is available at http://www.wikidata.org/wiki/Wikidata:Contact_the_development_team/Archive/2013/04#Transitive_properties_and_SPARQL.
There are important details that would need to be worked out with conflicting sources and qualifiers, but I'm filing this here so there's a place to track this feature request at a high level.