Why Teamviewer keeps running in the background?

Because that is the nature of teamviewer: it is build to respawn.

/opt/teamviewer8/tv_bin/script/teamviewerd.sysv is probably responsible for it.

To stop teamviewer use:

sudo teamviewer --daemon stop 

It will show ...

initctl stop teamviewerd
teamviewerd stop/waiting

and it is gone ...

rinzwind@discworld:/opt/teamviewer8/tv_bin/script$ ps -ef|grep teamviewer
rinzwind 12712 12428  0 18:11 pts/0    00:00:00 grep --color=auto teamviewer

Commands to manipulate the daemon:

teamviewer --daemon status        show current status of the TeamViewer daemon
teamviewer --daemon start         start TeamViewer daemon
teamviewer --daemon stop          stop  TeamViewer daemon
teamviewer --daemon restart       stop/start TeamViewer daemon
teamviewer --daemon disable       disable TeamViewer daemon - don't start daemon on system startup
teamviewer --daemon enable        enable TeamViewer daemon - start daemon on system startup (default)

Regarding comment:

From teamviewer 9 help:

$teamviewer --help

 TeamViewer                      9.0.32150 

 teamviewer                      start TeamViewer user interface (if not running) 

 teamviewer --help               print this help screen 
 teamviewer --version            print version information 
 teamviewer --info               print version, status, id 
 teamviewer --ziplog             create a zip containing all teamviewer logs (useful when contacting support) 

 teamviewer --passwd [PASSWD]    set a password (useful when installing remote (ssh) 

 teamviewer --daemon status      show current status of the TeamViewer daemon 
 teamviewer --daemon start       start      TeamViewer daemon 
 teamviewer --daemon stop        stop       TeamViewer daemon 
 teamviewer --daemon restart     stop/start TeamViewer daemon 
 teamviewer --daemon disable     disable    TeamViewer daemon - don't start daemon on system startup 
 teamviewer --daemon enable      enable     TeamViewer daemon - start daemon on system startup (default) 

Options are still there in TV9.

If you install Teamviewer 10 from the .deb file, --daemon stop as recommended above won't work in Ubuntu 14.04 LTS (and others?). Don't know why.

The daemon is an 'upstart' job, so it gets controlled from /etc/init/teamviewerd.conf not /etc/init.d.

Unfortunately, for me, both initctl stop teamviewerd and service teamviewerd stop result in:

initctl: Unknown instance: 

teamviewerd.sysv gets installed in /opt. So, to stop it, you need to do:

$ sudo /opt/teamviewer/tv_bin/script/teamviewerd.sysv stop

systemctl stop teamviewerd.service
systemctl disable teamviewerd.service

Here is the script "teamviewer.bash" I am using and that works in 14.04:

#!/bin/bash
# to be copied to /opt/teamviewer/tv_bin/script
# modify /usr/share/applications/teamviewer-teamviewer11.desktop :
# Exec=bash /opt/teamviewer/tv_bin/script/teamviewer.bash
# sudo visudo
# add:
# user ALL=(ALL:ALL) NOPASSWD:/opt/teamviewer/tv_bin/script/teamviewer
# sudo service sudo restart
echo 'teamviewer --daemon enable' | sudo sh && \
/opt/teamviewer/tv_bin/script/teamviewer && \
echo 'teamviewer --daemon disable' | sudo sh

teamviewer is using upstart to fire up the daemon at boot. The upstart does have a respawn set to keep a process running. As a 12.04 user mentioned, respawn stanzas in the upstart script are probably what you want to comment out.

The teamviewer process is/will run as root if fired up upstart. Since the respawn is in the upstart script you could have issues killing it permanently whether you do an implicit kill or 'sudo stop teamviwer' (the upstart way) or 'sudo teamviewer --daemon status'. Your best bet is probably just to comment out respawn lines in the upstart script, then start and stop as the service as needed.