If you try the Arch Linux image you can get docker going, as smokes2345 says you cant use much in the docker repo but you can create your own stuff and it'll run. Docker was at 1.5 at the time of writing so its quite up-to-date too.
As I understand the Docker hub/repo is x86_64 only at the moment, and doesn't work too well for 32 bit Intels either.
Whilst its a bit uphill you can build a base image from the Arch Raspberry pi tar file using [docker import][1] then create a dockerfile to make it 'do stuff'.
I've had it running sqlite3 and python3 in a container, admittedly that's pretty lame but it does work.
The below is very much 'what-if?' the image is about 1GB but hopefully gets you going. this assumes you are root and you've updated arch with
pacman -Syy
pacman -Su
Anyway, to build my base image I did
# install docker and lxc
pacman -S docker lxc
# download the arch image
wget http://archlinuxarm.org/os/ArchLinuxARM-rpi-2-latest.tar.gz
# build a base image from it
cat ArchLinuxARM-rpi-2-latest.tar.gz | docker import - archarm:test2
it takes a minute or two but you should then see something like
14959a4d75379ec943f6303a59109aebe1763971586812cd074f652c466cf16d
and if you type
docker images
you should see
archarm test2 14959a4d7537 6 minutes ago
with the start of that long ID - yours will be different.
you should then be able to run this image as a container using
docker run -t -i --name toby archarm:test2 /bin/bash
and there is Arch on the Pi2 running a container :)
For a slightly less trivial example if you create a Dockerfile in a directory and add
#use base image
FROM archarm:test2
#update to get the right urls
RUN pacman -Syy
#fetch sqlite
RUN pacman -S sqlite3 --noconfirm
ENTRYPOINT sqlite3 testdb
then build this using
docker build --tag arch:sqlite3 .
you should be able to start a container directly into Sqlite3
docker run --name toby8 -t -i arch:sqlite3
[toby@archpi sqlite]$ docker run --name toby8 -t -i arch:sqlite3
SQLite version 3.8.9 2015-04-08 12:16:33
Enter ".help" for usage hints.
sqlite>
Hope that helps.
And yes, Ubuntu Snappy on the Pi2 seems a bit pointless out-of-the-box
[1]: http://docs.docker.com/reference/commandline/cli/#import