Various players are available:
xine: a free video player
ogle: DVD player.
okle: KDE version of ogle
mplayer: Movie Player for Linux
totem: plays both audio and video files, audio CDs, VCD and DVD.
realplay: from RealNetworks.
hxplay: a Real alternative, see HelixDNA.
kaffeine: media player for KDE3.
Most likely, you will find one of these in your graphical menus.
Keep in mind that all codecs necessary for viewing different types of video might not be on your system by default. You can get a long way downloading W32codecs and libdvdcss.
The LDP released a document that is very appropriate for this section. It is entitled DVD Playback HOWTO and describes the different tools available for viewing movies on a system that has a DVD drive. It is a fine addition to the DVD HOWTO that explains installation of the drive.
For watching TV there is choice of the following tools, among many others for watching and capturing TV, video and other streams:
tvtime: great program with station management, interaction with teletext, film mode and much more.
zapping: Gnome-specific TV viewer.
xawtv: X11 TV viewer.