How do I speed up counting rows in a PostgreSQL table?

For a very quick estimate:

SELECT reltuples FROM pg_class WHERE relname = 'my_table';

There are several caveats, though. For one, relname is not necessarily unique in pg_class. There can be multiple tables with the same relname in multiple schemas of the database. To be unambiguous:

SELECT reltuples::bigint FROM pg_class WHERE oid = 'my_schema.my_table'::regclass;

If you do not schema-qualify the table name, a cast to regclass observes the current search_path to pick the best match. And if the table does not exist (or cannot be seen) in any of the schemas in the search_path you get an error message. See Object Identifier Types in the manual.

The cast to bigint formats the real number nicely, especially for big counts.

Also, reltuples can be more or less out of date. There are ways to make up for this to some extent. See this later answer with new and improved options:

• Fast way to discover the row count of a table in PostgreSQL

And a query on pg_stat_user_tables is many times slower (though still much faster than full count), as that's a view on a couple of tables.

Count is slow for big tables, so you can get a close estimate this way:

SELECT reltuples::bigint AS estimate 
FROM pg_class 
WHERE relname='tableName';

and its extremely fast, results are not float, but still a close estimate.

• reltuples is a column from pg_class table, it holds data about "number of rows in the table. This is only an estimate used by the planner. It is updated by VACUUM, ANALYZE, and a few DDL commands such as CREATE INDEX" (manual)
• The catalog pg_class catalogs tables and most everything else that has columns or is otherwise similar to a table. This includes indexes (but see also pg_index), sequences, views, composite types, and some kinds of special relation (manual)
• "Why is "SELECT count(*) FROM bigtable;" slow?" : http://wiki.postgresql.org/wiki/FAQ#Why_is_.22SELECT_count.28.2A.29_FROM_bigtable.3B.22_slow.3F