Just had a reminder of that this morning... Was doing a bit of routine maintenance on the server at work when I noticed repeated ssh login attempts appearing in the system logs... with usernames that clearly don't exist. Tracing the source ip address sent me to Beijing somewhere, so someone there was trying a port scan and random ssh login attempts.

I've never really looked for this kind of interaction before, and I wonder just how common it is these days - but I'd say that you can now pretty much guarantee that it will happen at some stage, and you'd better hope your security is up to the task.