Try:
SELECT
[TableName] = so.name,
[RowCount] = MAX(si.rows)
FROM
sysobjects AS so,
sysindexes AS si
WHERE
so.xtype = 'U'
AND
si.id = OBJECT_ID(so.name)
GROUP BY
so.name
ORDER BY
2 DESC
This is the indexed rows. This is probably only an approximation, as databases change a lot and some stuff might not be indexed, but this will be fast.
EDIT: Note that so.xtype is user types, making the assumption you do not want the system stuff and only "real" data stuff.
EDIT2: no flames note: probably a bad idea to query on the sysobjects table :).
EDIT3: to specifically address requirement, and no associative joins :)
SELECT sum(mycount) from
(SELECT
MAX(si.rows) AS mycount
FROM
sysobjects AS so
join sysindexes AS si on si.id = OBJECT_ID(so.name)
WHERE
so.xtype = 'U'
GROUP BY
so.name
) as mylist