How to execute SQL against all DBs on a Server

sp_MSForEachDB

One option is sp_MSForEachDB. It's undocumented but useful nonetheless

DECLARE @command varchar(1000) 
SELECT @command = 
    'USE [?] UPDATE Table1 SET Field1 = ''ninjas'' WHERE Field2 = ''pirates''' 
EXEC sp_MSforeachdb @command

A search of the interwebs has many more examples too

Note: Being an unsupported function (which has some known bugs) you may want to write your own version (thanks @Pradeep)

---

The SQL example above would need to be restructured as:

DECLARE @findKeySQL nvarchar(2000)
DECLARE @searchKey nvarchar(20)

SET @searchKey = lower('%remote%')

SET @findKeySQL = 'IF ''[?]'' NOT IN (''[master]'', ''[model]'', 
                                     ''[msdb]'', ''[tempdb]'')
        select 
            so.name,
            so.type,
            @@ServerName as Server,
            ''?'' as DBName 
        from
            [?].dbo.sysobjects so with (nolock)
            join [?].sys.all_sql_modules sc with (nolock) on so.id = sc.object_id
        where (lower(sc.definition) like ''' + @searchKey + ''')
        group by so.name, so.type
        order by so.type, so.name'

EXEC sp_MSForEachDB @findKeySQL

NOTES:

1. ? is replaced in the query as the database name, so structure the query to explicitly define which DB it is to query against
2. modified to use sys.all_sql_modules as holds complete module text (syscomments could split the keyword when reach the spanning over rows)

Just my $0.05: SQL Multi Script (execution of multiple scripts against multiple SQL Servers).

SSMS Tools Pack does this nicely and it is free for database servers prior to 2012. The feature: "Run on Multiple Targets" - http://www.ssmstoolspack.com/Features?f=6