As this question looks useful to me, I have created it in order to provide an answer. (The meta issue of doing this was discussed and answered (here and here).
There are different methods for this.
1. SMPlayer.
and the Youtube Browser

sudo add-apt-repository ppa:rvm/smplayer
sudo apt-get update
sudo apt-get install smplayer smtube

It starts the separate application, SMPlayer Youtube Browser, to search for videos. One can create a link/desktop launcher to it,

or just run
smtube
2. Using VLC. It looks like VLC is able to start videos of this kind from more websites, while smplayer is limited to youtube.

One can add the link to the video in VLC

3. Using Totem:

Some plugins are available for Totem player, among which a youtube browser similar to that of SMPlayer. You can open youtube videos in Totem, at lower quality it seems than in the previous options, but they load faster and are perfect for listening music from youtube.

There is also an arte-tv plugin for Totem that is not working at the moment... but maybe it will in the future... and supplementary plugins, including a BBC iPlayer. (The later no better than the one for arte-tv I fear.)
But there is a more elegant method:
using add-ons/extensions to open the external players directly from the internet browser's interface or context menu.
Firefox Openwith addon, created initially to open links in different web browsers, can do just that, by adding in its Preferences vlc and smtube instead of/beside browsers .

In Chromium there is an extension to start youtubes in VLC - here.
To use it, the youtube video has to be playing, the VLC web interface has to be enabled (VLC Tools-Preferences-Show Settings -All-Interface-Main-enable Web, restart VLC) and VLC has to be already open.


While VLC seems able to do this outside youtube, it has limitations when dealing with other websites. In Dailymotion works perfectly, but on Google videos it already may have problems, in others it's the OpenWith addon that would not work. I hadn't time to test them enough, I'll update this post in time, and invite comments and edits that would help find ways to open any embedded flash in VLC or other external player.
(This answer was based on ideas coming from izx, Halknner and user55822 as they answered or commented on other question.)
There is a VLC add-on to play YouTube videos and playlists - here
Copy the URL of the youtube video or playlist (must contain "list=PL...")
Start VLC, press Ctrl+N, paste the url then click on "Play" (or Alt+P then Enter), the video /playlist should start.

In 'Media', 'Save Playlist to File' and may open it later in VLC.