Only on recent hardware. My dad had an older iMac that was aged, but not unusable. He got a new iPhone, which required the newest version of iTunes, which further required an upgrade of the OS to 10.8, which was blocked because he didn't meet minimum system requirements.

It's free, but only after you pay for new hardware.

Exactly what happened to me. Ended up using the new iTunes in a VM running... Windows XP. How's that for irony. iTunes couldn't run on Leopard, but could run on something much older and in a resource-limited VM. Obviously my Core2 Duo was still capable of running iTunes.

I finally had to buy a Mac mini just so I could do iOS development. But every Mac I buy now, I just have to plan on running Linux on it in a few years.

absolutely not, i had to pay to upgrade Leopard to the next OS.

You can upgrade to OS X Mavericks from Snow Leopard (10.6.8), Lion (10.7), or Mountain Lion (10.8). (for free)

https://www.apple.com/osx/how-to-upgrade/

If you only had Leopard you had to spend $20 to get Snow Leopard first before getting the update to Mavericks.

Edit: I should say that not all Snow Leopard machines can be upgrade to Mavericks, a bunch of the 2006 models can't.