Note that LIKE will work either case-sensitively or case-insensitively depending upon which collation is in effect for the expression, but in your case, you have specified no wildcards so there is little point looking to use LIKE.
The default SQL Server installation is case-insensitive.
If you want a case-insensitive compare because you've got a case-sensitive database, you can cast.  I believe this is the appropriate syntax (I've never used it for an IN list on one side of an expression, though).
SELECT *
FROM emailaddresses
WHERE addr COLLATE SQL_Latin1_General_CP1_CI_AS 
IN (
    'john@google.com' COLLATE SQL_Latin1_General_CP1_CI_AS
    ,'jim@google.com' COLLATE SQL_Latin1_General_CP1_CI_AS
)
A real case for LIKE would be something for something like addr LIKE '%@google.com"