Your media player.

It's simple to download, install, and so on.

To be honest, you don't even need to search for anything if you're using one of the latest versions of Winamp. Launch library mode, add all your music there, right-click on the album you're interested in, and select "Get Album Art" (or something similar, like "get cover art," if you're using the Russian version). Winamp finds covers for well-known foreign bands without any problems; it's more difficult with iTunes – you either need to register with the iTunes Store or do it manually (I've already gotten used to doing it myself because the covers found by players aren't always of the desired resolution and quality).

But what I don't like about this program (at least when using it with an iPod) is that it somehow converts all the music, and after processing, it becomes very difficult to extract the music back.

Hmm... Maybe I misunderstood you, but iTunes and the iPod work perfectly well with the MP3 format we're used to, and there's no need to convert anything. All the tracks added to the library are copied (or moved, depending on the settings) to a separate folder, from which it's also not difficult to extract them.

Let's say the system on the computer was reinstalled, and you want to restore your music collection, but in this case, you'll have to put in some effort, or just use iTunes.

I don't quite understand this. To transfer the library intact to another Windows or another computer, you have to create a backup of it on rewritable discs (this is especially necessary if you want to save the play count, ratings, added lyrics, and other unique settings that are not written in ID3 tags)