Find the last time table was updated

If you want to see data updates you could use this technique with required permissions:

SELECT OBJECT_NAME(OBJECT_ID) AS DatabaseName, last_user_update,*
FROM sys.dm_db_index_usage_stats
WHERE database_id = DB_ID( 'DATABASE')
AND OBJECT_ID=OBJECT_ID('TABLE')

If you're talking about last time the table was updated in terms of its structured has changed (new column added, column changed etc.) - use this query:

SELECT name, [modify_date] FROM sys.tables

If you're talking about DML operations (insert, update, delete), then you either need to persist what that DMV gives you on a regular basis, or you need to create triggers on all tables to record that "last modified" date - or check out features like Change Data Capture in SQL Server 2008 and newer.