First, an example is Foobar2000 in Wine. Foobar2000 has different ways of displaying media library, my favorites being Album list (foo_albumlist, component installed by default) and especially Facets (foo_facets, component to be manually installed). I am aware that finding something better than Foobar2000 is unlikely. The downside of Foobar is of course using Wine, which makes it unstable, resource-hungry, and ugly-looking.
Quod Libet, once the media library folder selected, displays this folder separately in the list of folders (if "View" - "File System" is selected). Then, this folder can be browsed, but the way of doing that is clumsy, sluggish, and there are no tabs for playlists, nor other way of quickly accessing playlists (that I'm aware of).
My favourite Ubuntu music player is DeadBeef, which has a plugin called File Browser (64x version here) that displays the media library as folder structure.
(Considering the editing of this answer: as I was for a while in the beta version of 12.10 quantal which was not yet fully supported, the player could not be installed from PPA, and the version of the file browser stopped working from time to time in portable/static version in quantal (the player as such worked ok). That was the initial reason for posting this question. But getting back into a stable version of Lubuntu, Deadbeef is no 1 again and I think it deserves a more detailed presentation.)
The file-browser plugin is gtk2 so it would work only with the gtk2 GUI of the browser (Deadbeef 0.5.6 allows a gtk3 gui switch)
Also, this plugin is incompatible with the gtk2 version of the plugin called Infobar (x86_64 version here) that would display lyrics (see this related answer). Infobar has a gtk3 version. A workaround for using the two plugins alternatively is installing filebrowser plugin and the gtk3 version of infobar: in this way changing the player's gui would switch between the two plugins too.
To install Deadbeef plugins (
.so files): they have to be copied into a folder. On their site they say:
~/.local/lib/deadbeef/. But in fact, in (L)Ubuntu, in the case of Deadbeef installation from PPA the plugin file should be put into:
/usr/lib/deadbeef, while after the player's installation from .deb the plugins go to:
/opt/deadbeef/lib/deadbeef. In static-portable builds:
Deadbeef player has playlist tabs but no library search (as far as I know).
Clementine is an excellent player (no matter it having a screaming-orange tray icon that violates my monotone icon set). But when it comes to seeing the media library folders it cannot do it: if I want to see that, I have to select "Files" instead of "Library", and go to /media/username/externaldrivename and look there. But it has the very clever quality that after restart it can remember last path used in this way. (The player has playlist tabs and a search feature that does not work... Or does it? Not in my case, though I'd seen it said it does. Anyway, Clementine looks like a good option for what is asked here.)
I will not hurry setting a definitive answer for some time as I want to see as many answers as possible.
I cannot help posting here a screenshot of taskmanager with different players working at the same time (which i'll update in time). I guess this matter has a certain importance in making an opinion about software.