You can see object-level permissions using this query: the commented-out section in the WHERE clause will limit the results to the VIEW DEFINITION permission.

SELECT 
    o.name AS ObjectName,
    su.name AS LoginName,
    dp.permission_name AS PermissionType,
    dp.state_desc AS PermissionStatus
FROM 
    sys.database_permissions dp
     INNER JOIN 
    sys.objects o ON 
        dp.major_id = o.object_id
     INNER JOIN 
    sys.sysusers su ON 
        dp.grantee_principal_id = su.uid
--WHERE dp.[type] = 'vw'
ORDER BY o.name

I get null as a result. Does anyone knows what may be wrong here?

You need the VIEW DEFINITION permission, otherwise you get an empty result set.

Use can use sys.fn_my_permissions or HAS_PERMS_BY_NAME to get the relevant permission on a database for the current user:

HAS_PERMS_BY_NAME:

SELECT HAS_PERMS_BY_NAME(null, 'DATABASE', 'VIEW DEFINITION');

You get a simple 0 or 1 as a result of this query.

sys.fn_my_permissions

SELECT * FROM sys.fn_my_permissions(NULL, 'DATABASE') 
WHERE permission_name = N'VIEW DEFINITION'

The result set for this query looks like this:

With impersonation

If you have the IMPERSONATE permission, you can even check it for another user:

EXECUTE AS USER = 'otheruser'
SELECT HAS_PERMS_BY_NAME(null, 'DATABASE', 'VIEW DEFINITION');  
REVERT

or

EXECUTE AS USER = 'otheruser';
SELECT * FROM sys.fn_my_permissions(NULL, 'DATABASE')
WHERE permission_name = N'VIEW DEFINITION'
REVERT

Two things:

1. Use sp_helptext: it's a lot easier than jumping through system tables.
2. You can use sys.fn_my_permissions to see what permissions you have on any object.