A LiveCD is a bootable CD containing a fully operational version of an operating system, but can be run without installing its contents to the target computer. The user can perform normal tasks, such as web surfing, chat, playing games, or can use the LiveCD as a recovery environment in the event of failure of an installed system.
Linux distributions usually provide the contents of a LiveCD as a large .iso file. This contains a disk image of the CD-ROM or DVD-ROM including its boot sector in the standard "ISO image" format. There are disk-writing programs for most operating systems that can burn the .iso image to a recordable disk.
Booting from USB
Often, there are provisions for putting a LiveCD's contents onto a USB flash drive to use as a boot device as opposed to a writable disk.
Fedora and Ubuntu have programs that automate this, liveusb-creator and usb-creator. These programs also have options to allow the Live USB to retain alterations made to it.
Distributions using LiveCD
This list is largely incomplete; especially the latter, since many distributions offer a LiveCD environment for install.
Distros that are primarily or only LiveCDs
Distros that use a LiveCD environment to install