Script that provides the row counts and table names

-- Shows all user tables and row counts for the current database 
-- Remove OBJECTPROPERTY function call to include system objects 
SELECT o.NAME,
  i.rowcnt 
FROM sysindexes AS i
  INNER JOIN sysobjects AS o ON i.id = o.id 
WHERE i.indid < 2  AND OBJECTPROPERTY(o.id, 'IsMSShipped') = 0
ORDER BY o.NAME

If you're on SQL Server 2005 or newer (you unfortunately didn't specify which version of SQL Server you're using), this query should give you that information:

SELECT 
    TableName = t.NAME,
    TableSchema = s.Name,
    RowCounts = p.rows
FROM 
    sys.tables t
INNER JOIN 
    sys.schemas s ON t.schema_id = s.schema_id
INNER JOIN      
    sys.indexes i ON t.OBJECT_ID = i.object_id
INNER JOIN 
    sys.partitions p ON i.object_id = p.OBJECT_ID AND i.index_id = p.index_id
WHERE 
    t.is_ms_shipped = 0
GROUP BY
    t.NAME, s.Name, p.Rows
ORDER BY 
    s.Name, t.Name

This produces an output something like (this is from AdventureWorks):

TableName       TableSchema      RowCounts
AWBuildVersion    dbo                  1
DatabaseLog       dbo               1597
ErrorLog          dbo                  0
Department        HumanResources      16
Employee          HumanResources     290
JobCandidate      HumanResources      13
Address           Person           19614
AddressType       Person               6
... and so on......