My philosophy is always ask for jobs that aren't listed. If I'm applying for a job, there could be anywhere between 1 and 1,000 other people applying. Those aren't good odds of even getting a glance.

If you had applied and asked if you could work for them as an intern, even though they hadn't mentioned it anywhere, chances are there would be one applicant... you.

You get brownie points for taking initiative, taking a risk, and best of all - there is no other competition to distract them from you.