MP3shki.ru does both. It crawls for music at websites like Youtube or Last.fm and is hosted in Russia. The interface is one of the best that I have seen yet, graphics and usability is awesome. Begin by clicking on the little EN link on top to switch to the English user interface, makes it easier.

Then search for an artist or song and watch how the search results are populated on the same page. A click on a search result opens a tiny overlay menu with options to play the song, add it to the playlist, to view the source and the link to the song and to mark it bad.

Songs can also be dragged and dropped into the playlist. It is furthermore possible to create more than one playlist, I suppose you can save them if you register an account.

If you click on the icon before the song title you add it to your playlist which can be saved, shared and embedded. Instead of trying out random finds you can also perform a search for an artist, band name or title and add those found to your playlist as well.

This means that is is relatively easy to build a large playlist with songs that you like and listen to them while online. The link to the song is displayed as well but not clickable by default.

There is however the possibility to use a program like Grab++ to grab the link and send it to a download manager such as Orbit downloader to download the song. I tested this method and it works perfectly.