Internet libraries are an excellent idea, and would be a large step toward solving the problem of illegal internet downloads.
Let's first look at the analog world. Here in real life, there are three options if someone wants to get a book, listen to music, or watch a movie. He must either 1) pay for it, either by buying at a store or watching in a theatre, 2) steal it, or 3) check it out from a library. All three options have their downside. Number one costs money, number two risks punishment and/or moral degeneration, and number three is temporary, takes longer, and sometimes doesn't work, if the book or dvd is rare.
Now, over on the online world, there are only two options if someone wants music, a movie, or a book. He must either 1) pay for it (through iTunes, Kindle, ect.) or 2) steal it. There is very little downside to stealing, as it is nearly impossible to be punished for it. Although some music companies have tried to sue people who have illegally downloaded music, their efforts haven't made a significant difference, since there are hundreds of millions of people, and they can only sue a handful. Depending on your point of view, some of the moral problems with stealing music online are diminished, too, since no one actually loses the music, you just make a copy.
But think about it. With libraries, the real world has presented an extra option, which everyone is satisfied with. Technically, authors everywhere should be complaining, since libraries only pay for a book once, but then lend it to hundreds of people, who all read it. The author only gets one royalty even though he is read hundreds of times. This is the same thing that happens online, where music is only bought once, but is then distributed to thousands of other people. But at libraries, nobody complains. Why? Because people are used to it, and everyone expects it. And also because authors know that the word-of-mouth will help them become more prolific.
So, since libraries work so well in the real world, I think it's high time that we got some electronic versions on the internet. People who don't want to steal, but also can't afford to buy everything they want would finally have another option. In addition, one of the problems with physical libraries would be solved; no wait time. There would still be a few downsides to it; the more rare things will probably still be hard to find, and I would recommend making the downloads temporary, in keeping with physical libraries.
And yes, before anyone mentions it, I do know that there are a few online libraries available. None of them have nearly as large a collection of books, and I don't know of any that offer movies and music.