It will be marked as experimental for a long time. There isn't a magical point at which it will suddenly be perfect and bug free. That said kernel 3.2 was a major point of stability.
https://btrfs.wiki.kernel.org/index.php/FAQ#Is_btrfs_stable....It is integrated with the package manager on Ubuntu already. I just upgraded my laptop to Quantal and part of the upgrade process spotted I was using btrfs and created a snapshot. (It was a complete waste of time as I have automatically created hourly, daily, weekly and monthly snapshots.) Doing regular package updates is very slow with btrfs. This is due to fsync() being called several times per file.
You'll also want Quantal for an updated btrfs-tools package. For example it lets you do scrubbing. You also need it (and kernel 3.3+) to change raid levels after filesystem creation. The Ubuntu 12.04 installer does create and install to btrfs but didn't let you configure things like raid level so you were stuck with whatever it did.
I've been running all my systems on btrfs for several months now on Ubuntu 12.04 (kernel 3.2) on both SSD and HDD including using RAID 0, RAID 1, dmcrypt/LUKS, inplace conversion from ext4 and who knows what else. (Across my server, workstation, laptop and HTPC.)
The only problem I have had is when filesystems fill up. I've never lost data but it can be quite frustrating trying to find files to delete (also need to be removed from snapshots), rebalancing etc to get things running smoothly again. The various ways of doing df are mostly a work of fiction.
My data is duplicated to offline backups, Dropbox, multiple systems and git/hg repositories so the failure of any system would be annoying but I'd never lose anything. You should make sure you are in that position first, independent of what filesystems are being used.