MongoDB ‘count()’ is very slow. How do we refine/work around with it?

There is now another optimization than create proper index.

db.users.ensureIndex({name:1});
db.users.find({name:"Andrei"}).count();

If you need some counters i suggest to precalculate them whenever it possible. By using atomic $inc operation and not use count({}) at all.

But mongodb guys working hard on mongodb, so, count({}) improvements they are planning in mongodb 2.1 according to jira bug.