Bonjour,
J'ai voulu installer "proprement" Docker comme décrit dans le tuto.
Et j'ai rencontré plus ou moins le même problème que @Sulsky sauf que je suis sous Debian 7.5 (Wheezy) chez OVH un KS-3.
Je précise que j'ai scrupuleusement suivi le tuto à la lettre.
La première chose qui diffère par rapport aux screens présents dans le tuto (mais je me suis dit que c'était propre à chaque système):

grub-mkconfig -o /boot/grub/grub.cfg
Generating grub configuration file ...
Found background image: /usr/share/images/desktop-base/desktop-grub.png
Found linux image: /boot/bzImage-3.14.27-xxxx-grs-ipv6-64
Found Debian GNU/Linux (stretch/sid) on /dev/sda2
done

A la suite de cela j'ai bien redémarré ma machine mais j'ai constaté que le service docker n'était pas lancé.
Et du coup j'ai lancé un :

service docker start
docker: unrecognized service

Après je me suis dit que j'allais le lancer manuellement et voire ce qu'il en retournait

docker daemon
WARN[0000] Udev sync is not supported. This will lead to unexpected behavior, data loss and errors. For more information, see https://docs.docker.com/reference/commandline/daemon/#daemon-storage-driver-option 
INFO[0000] API listen on /var/run/docker.sock           
WARN[0000] Usage of loopback devices is strongly discouraged for production use. Please use `--storage-opt dm.thinpooldev` or use `man docker` to refer to dm.thinpooldev section. 
INFO[0000] [graphdriver] using prior storage driver "devicemapper" 
WARN[0000] Running modprobe nf_nat failed with message: `modprobe: ERROR: ../libkmod/libkmod.c:578 kmod_search_moddep() could not open moddep file '/lib/modules/3.14.27-xxxx-grs-ipv6-64/modules.dep.bin'`, error: exit status 1 
INFO[0000] Firewalld running: false                     
INFO[0000] Default bridge (docker0) is assigned with an IP address 172.17.0.1/16. Daemon option --bip can be used to set a preferred IP address 
WARN[0000] Your kernel does not support cgroup memory limit: mountpoint for memory not found 
WARN[0000] mountpoint for cpu not found                 
WARN[0000] mountpoint for blkio not found               
WARN[0000] mountpoint for cpuset not found              
FATA[0000] Error starting daemon: Devices cgroup isn't mounted

C'est là que je me suis dit que ça ressemblait pas mal à ce qu'avait eu @Sulsky sauf que si j'ai bien compris la commande

apt-get install lxc cgroup-lite

n'est pas pour mon système Debian et de toute façon il retourne

Reading package lists... Done
Building dependency tree       
Reading state information... Done
Package cgroup-lite is not available, but is referred to by another package.
This may mean that the package is missing, has been obsoleted, or
is only available from another source
E: Package 'cgroup-lite' has no installation candidate

Et pour plus d'informations concernant mon environnement si ça peut aider

docker version
Client:
 Version:      1.9.1
 API version:  1.21
 Go version:   go1.4.3
 Git commit:   a34a1d5
 Built:        Fri Nov 20 17:56:04 UTC 2015
 OS/Arch:      linux/amd64
Cannot connect to the Docker daemon. Is the docker daemon running on this host?

mount
/dev/sda2 on / type ext4 (rw,relatime,errors=remount-ro,data=ordered)
devtmpfs on /dev type devtmpfs (rw,relatime,size=4035588k,nr_inodes=1008897,mode=755)
sysfs on /sys type sysfs (rw,nosuid,nodev,noexec,relatime)
tmpfs on /run type tmpfs (rw,nosuid,noexec,relatime,size=807224k,mode=755)
tmpfs on /run/lock type tmpfs (rw,nosuid,nodev,noexec,relatime,size=5120k)
proc on /proc type proc (rw,nosuid,nodev,noexec,relatime)
pstore on /sys/fs/pstore type pstore (rw,relatime)
configfs on /sys/kernel/config type configfs (rw,relatime)
tmpfs on /dev/shm type tmpfs (rw,nosuid,nodev,noexec,relatime,size=1719080k)
devpts on /dev/pts type devpts (rw,nosuid,noexec,relatime,gid=5,mode=620,ptmxmode=000)
/dev/sda3 on /home/user1 type ext4 (rw,relatime,data=ordered)
/dev/sda5 on /home/user2y type ext4 (rw,relatime,data=ordered)
binfmt_misc on /proc/sys/fs/binfmt_misc type binfmt_misc (rw,nosuid,nodev,noexec,relatime)
cgroup on /sys/fs/cgroup type tmpfs (rw,relatime,size=12k,mode=755)
cgmfs on /run/cgmanager/fs type tmpfs (rw,relatime,size=100k,mode=755)
systemd on /sys/fs/cgroup/systemd type cgroup (rw,nosuid,nodev,noexec,relatime,release_agent=/usr/lib/x86_64-linux-gnu/systemd-shim-cgroup-release-agent,name=systemd)
user@127.0.0.1:/cygdrive/C/Users/user/X2GO~1/S-2808~1/spool on /tmp/.x2go-root/spool/C-root-50-1452512931_stDmate-session_dp32 type fuse.sshfs (rw,nosuid,nodev,relatime,user_id=0,group_id=0,default_permissions)]

Si jamais quelqu'un a une idée... J'aimerai vraiment tester Docker.
Merci d'avance.

Voici ce que j'ai lorsque j'installe de cette façon

docker run hello-world
Unable to find image 'hello-world:latest' locally
latest: Pulling from library/hello-world

b901d36b6f2f: Extracting    601 B/601 B
0a6ba66e537a: Download complete 
Pulling repository docker.io/library/hello-world
975b84d108f1: Error pulling image (latest) from docker.io/library/hello-world, endpoint: https://registry-1.docker.io/v1/, Error mounting '/dev/mapper/docker-8:2-881285-3f12c794407e68e515ba7f473a744e748ac8a827a2ea8b33855dec564238b2e5' on 975b84d108f1: Error pulling image (latest) from docker.io/library/hello-world, Error mounting '/dev/mapper/docker-8:2-881285-3f12c794407e68e515ba7f473a744e748ac8a827a2ea8b33855dec564238b2e5' on '/var/lib/docker/devicemapper/mnt/3f12c794407e68e515ba7f473a744e748ac8a827a2ea8b33855dec564238b2e5': invalid argument 

Error pulling image (latest) from docker.io/library/hello-world, Error mounting '/dev/mapper/docker-8:2-881285-3f12c794407e68e515ba7f473a744e748ac8a827a2ea8b33855dec564238b2e5' on '/var/lib/docker/devicemapper/mnt/3f12c794407e68e515ba7f473a744e748ac8a827a2ea8b33855dec564238b2e5': invalid argument

J'ai cherché sur le web comment résoudre ce problème et toutes les solutions trouvées n'ont pas fonctionné...

Le le /etc/init.d/docker. demandé

#!/bin/sh
set -e

### BEGIN INIT INFO
# Provides:           docker
# Required-Start:     $syslog $remote_fs
# Required-Stop:      $syslog $remote_fs
# Should-Start:       cgroupfs-mount cgroup-lite
# Should-Stop:        cgroupfs-mount cgroup-lite
# Default-Start:      2 3 4 5
# Default-Stop:       0 1 6
# Short-Description:  Create lightweight, portable, self-sufficient containers.
# Description:
#  Docker is an open-source project to easily create lightweight, portable,
#  self-sufficient containers from any application. The same container that a
#  developer builds and tests on a laptop can run at scale, in production, on
#  VMs, bare metal, OpenStack clusters, public clouds and more.
### END INIT INFO

export PATH=/sbin:/bin:/usr/sbin:/usr/bin:/usr/local/sbin:/usr/local/bin

BASE=docker

# modify these in /etc/default/$BASE (/etc/default/docker)
DOCKER=/usr/bin/$BASE
# This is the pid file managed by docker itself
DOCKER_PIDFILE=/var/run/$BASE.pid
# This is the pid file created/managed by start-stop-daemon
DOCKER_SSD_PIDFILE=/var/run/$BASE-ssd.pid
DOCKER_LOGFILE=/var/log/$BASE.log
DOCKER_OPTS=
DOCKER_DESC="Docker"

# Get lsb functions
. /lib/lsb/init-functions

if [ -f /etc/default/$BASE ]; then
	. /etc/default/$BASE
fi

# Check docker is present
if [ ! -x $DOCKER ]; then
	log_failure_msg "$DOCKER not present or not executable"
	exit 1
fi

check_init() {
	 # see also init_is_upstart in /lib/lsb/init-functions (which isn't available in Ubuntu 12.04, or we'd use it directly)
	 if [ -x /sbin/initctl ] && /sbin/initctl version 2>/dev/null | grep -q upstart; then        
                log_failure_msg "$DOCKER_DESC is managed via upstart, try using service $BASE $1"
                exit 1
         fi
}

fail_unless_root() {
	if [ "$(id -u)" != '0' ]; then
		log_failure_msg "$DOCKER_DESC must be run as root"
		exit 1
	fi
}

cgroupfs_mount() {
	# see also https://github.com/tianon/cgroupfs-mount/blob/master/cgroupfs-mount
	if grep -v '^#' /etc/fstab | grep -q cgroup \
		|| [ ! -e /proc/cgroups ] \
		|| [ ! -d /sys/fs/cgroup ]; then
		return
	fi
	if ! mountpoint -q /sys/fs/cgroup; then
		mount -t tmpfs -o uid=0,gid=0,mode=0755 cgroup /sys/fs/cgroup
	fi
	(
		cd /sys/fs/cgroup
		for sys in $(awk '!/^#/ { if ($4 == 1) print $1 }' /proc/cgroups); do
			mkdir -p $sys
			if ! mountpoint -q $sys; then
				if ! mount -n -t cgroup -o $sys cgroup $sys; then
					rmdir $sys || true
				fi
			fi
		done
	)
}

case "$1" in
	start)
		check_init
		
		fail_unless_root

		cgroupfs_mount

		touch "$DOCKER_LOGFILE"
		chgrp docker "$DOCKER_LOGFILE"

		ulimit -n 1048576
		if [ "$BASH" ]; then
			ulimit -u 1048576
		else
			ulimit -p 1048576
		fi

		log_begin_msg "Starting $DOCKER_DESC: $BASE"
		start-stop-daemon --start --background \
			--no-close \
			--exec "$DOCKER" \
			--pidfile "$DOCKER_SSD_PIDFILE" \
			--make-pidfile \
			-- \
				daemon -p "$DOCKER_PIDFILE" \
				$DOCKER_OPTS \
					>> "$DOCKER_LOGFILE" 2>&1
		log_end_msg $?
		;;

	stop)
		check_init
		fail_unless_root
		log_begin_msg "Stopping $DOCKER_DESC: $BASE"
		start-stop-daemon --stop --pidfile "$DOCKER_SSD_PIDFILE" --retry 10
		log_end_msg $?
		;;

	restart)
		check_init
		fail_unless_root
		docker_pid=`cat "$DOCKER_SSD_PIDFILE" 2>/dev/null`
		[ -n "$docker_pid" ] \
			&& ps -p $docker_pid > /dev/null 2>&1 \
			&& $0 stop
		$0 start
		;;

	force-reload)
		check_init
		fail_unless_root
		$0 restart
		;;

	status)
		check_init
		status_of_proc -p "$DOCKER_SSD_PIDFILE" "$DOCKER" "$DOCKER_DESC"
		;;

	*)
		echo "Usage: service docker {start|stop|restart|status}"
		exit 1
		;;
esac

Lorsque je lance docker daemon j'ai :

INFO[0000] API listen on /var/run/docker.sock           
WARN[0000] Usage of loopback devices is strongly discouraged for production use. Please use `--storage-opt dm.thinpooldev` or use `man docker` to refer to dm.thinpooldev section. 
INFO[0000] [graphdriver] using prior storage driver "devicemapper" 
WARN[0000] Running modprobe nf_nat failed with message: `modprobe: ERROR: ../libkmod/libkmod.c:578 kmod_search_moddep() could not open moddep file '/lib/modules/3.14.27-xxxx-grs-ipv6-64/modules.dep.bin'`, error: exit status 1 
INFO[0000] Firewalld running: false                     
INFO[0000] Default bridge (docker0) is assigned with an IP address 172.17.0.1/16. Daemon option --bip can be used to set a preferred IP address 
WARN[0000] Your kernel does not support kernel memory limit. 
WARN[0000] Your kernel does not support cgroup cfs period 
WARN[0000] Your kernel does not support cgroup cfs quotas 
INFO[0000] Loading containers: start.                   

INFO[0000] Loading containers: done.                    
INFO[0000] Daemon has completed initialization          
INFO[0000] Docker daemon                                 commit=a34a1d5 execdriver=native-0.2 graphdriver=devicemapper version=1.9.1

La technique fonctionne bien je me suis basé sur le docker https://hub.docker.com/r/mattiash/data/
Je n'ai pas cette erreur sur d'autre serveur ...