My hard drive malfunctioned and I had to have it replaced with a new one and reboot my Mac. Now iPhoto, iMovie and garage band have all disappeared and are no longer on my Mac. Is there any way to get them back without having to pay for them?
Log into the App Store, and they should be there in the 'Purchases' tab - assuming that when you bought the Mac you told the Store that you wanted to register the apps to your Apple ID.
The apps aren't part of the OS - so you will need to use the same Apple ID as you used to "redeem" them initially. If you feel you didn't redeem them, you could contact Apple support and ask for them to check if the included apps for that Mac have been claimed. If not, I would expect them to get you redemption codes to not have to pay for them if they should be included.
If someone redeemed them, it's up to Apple whether they decide to slide you them gratis or ask for you to purchase them - but it wouldn't hurt to ask nicely.
You cannot ever get them back if they're not in the purchases >-<