You can use INFORMATION_SCHEMA.TABLES to retrieve information about your database tables.
As mentioned in the Microsoft Tables Documentation:
INFORMATION_SCHEMA.TABLESreturns one row for each table in the current database for which the current user has permissions.
The following query, therefore, will return the number of tables in the specified database:
USE MyDatabase
SELECT COUNT(*)
FROM INFORMATION_SCHEMA.TABLES
WHERE TABLE_TYPE = 'BASE TABLE'
As of SQL Server 2008, you can also use sys.tables to count the the number of tables.
From the Microsoft sys.tables Documentation:
sys.tablesreturns a row for each user table in SQL Server.
The following query will also return the number of table in your database:
SELECT COUNT(*)
FROM sys.tables