Is there a stable Linux distro using btrfs?

openSUSE 11.3 has btrfs support, and is pretty awesome.

Btrfs has been developed to become the next generation default Linux file system. openSUSE is the first distribution that lets you choose Btrfs in the installer.

The installer will warn you that Btrfs is still experimental, so be cautious of using it on production system. You also have to remember to setup a separate /boot partition as the boot loader will not boot from a Btrfs partition yet.

openSUSE fanboi here

Debian supports it.

I've had it installed on a server of mine and running for about six months now. No issues, really.

Besides openSUSE, SUSE Linux Enterprise Server 11 SP2 provides support (not technology preview) for Btrfs.

Besides Btrfs, openSUSE 12.1 and SLE[SD]11SP2 also ships with the Snapper utility, which will help you manage snapshots. Both Snapper and its YaST plugin (yast snapper) provide the function to discover the content of a snapshot and the difference compared to another snapshot. The YaST disk partitioning module is also aware of Btrfs and will provide a recommended setup for subvolumes.

Ubuntu support Btrfs as well, quote from official ubuntu Btrfs

As of 11.04-beta1,
 it is possible to use only btrfs file systems with the caveat
 that grub _MUST_NOT_ be installed to the boot sector
 of the btrfs volume containing /boot.