Yes, that is possible when both computers are the same wired or wireless network and file sharing is enabled in System Preferences > Sharing > File Sharing.
When enabled, you see the other Mac in the Finder Sidebar and thus can log into that other Mac via that Mac's account credentials and share files back and forth.
I recently did so on the same wired and wireless network between a Mac running Mac OS X 10.6 Snow Leopard and a Mac running OS X 10.9 Mavericks.
Sharing files between Macs is quite easy and does not need that much configuration compared to sharing files between Mac OS X and Windows.