It seems like \'select count(*) from c\' in the SQL queries allowed by documentdb in the azure site and through the documentdb explorer (https://studiodocumentdb.codeplex.com/)
This is possible in the same way you write SQL query now,
SELECT VALUE COUNT(1) FROM myCollection
NOTE: COUNT(1) won't work for a huge datasets.
You can read more about supported queries from here
Just to recap - here is example of Count Stored Procedure via JS with continuation support.
And here is one more tool for DocumentDb that's pretty neat: https://github.com/mingaliu/DocumentDBStudio/releases
Upd Mar 2017: In the latest DDB SDK see DDB Aggregates press release there is full support for basic aggregates, without GROUP BY though (for now). Here is GIT REpo with examples: https://github.com/arramac/azure-documentdb-dotnet/tree/master/samples/code-samples/Queries