That question barely receives a “yes” in the real world, so I find myself stumped at why game creators think it's a good idea to put libraries in games.
Libraries are an attempt to give a player more information about a game world, in hopes that it'll make it more immersive. Most RPG libraries consist of history, news, and the creator's own version of fan fiction. I barely read history in reality. What makes game creators think I'll read it in a fantasy world where my only goal is to get enough cash to buy that super cool weapon that'll cut through a bus?
Let's take a look at different types of libraries in games.
Examples of Good Libraries:
Sims
These are there for two reasons: skills and entertainment. In the Sims 3, this comes in handy because you save a ton of money on buying books for skills. Also, these libraries have computers to perform extra tasks.
Harvest Moon
Great reference tool. Harvest Moon's library is for what plants grow when. It tells you how to play mini games, how to plant crops, and you can actually meet people in there.
Tomb Raider
Each book in Lara's Mansion in Tomb Raider: Anniversary has a clue to solving the next puzzle. Without the books, it makes it harder to play the game. The books actually have purpose and are necessary.
Examples of Bad Libararies:
Legend of Legaia
I'm in the middle of a mist-ridden society, trying to find an exit; I'm not going to read your stupid diary. Legend of Legaia's libraries are of little use. They are mainly people's diaries about the mist, or just useless information that I can't do anything with. The only positive point to these libraries is sometimes you find new battle combinations. That's really about it.
Legend of Dragoon
The main library in the game is full of information. Information I care nothing about. I've all ready sat through some elder giving me a “in the beginning” speech, and I don't feel like sitting through more of it. Long narrative CGs + giant libraries = zzzzzzz
Oregon Trail Version 745 (Or however many they have now)
This is a menu option in the game, where you can study different diseases and treatments according to the time period. As informative as this is, HOLY CRAP there's a lot to look at. None of this information, however, is incredibly critical to the game. You still get bitten by a snake and die.
My problem isn't with RPGs trying to get across more information. My problem is how loquacious game creators feel like being when they make libraries. The point of a game is to play. If you want to write fan fiction, put it on the internet like everyone else.
Ways to Get Across Information:
There are different ways to get across game world history in a game without resorting to long winded libraries:
Dialogue
If the information is critical to the story, slip it into the dialogue. Not with a “in the beginning” CG, but with a simple, “Remember how...” or “We haven't had a famine this bad since [this event in history].”
Townsfolk
Townsfolk are notorious for useless information. Short bouts of useless information. If you're going to give out non-essential information, the best thing to do it to keep it short and coming out of crazy, useless people.
Letters
Instead of having characters find diaries or go to libraries, have them find single sheets of paper in offices and houses that explain things. This increases the entertainment value and still gets the point across.
If you want libraries in your game, I have nothing against you. Just know that I probably won't be stopping by.
Libraries in games should be more for reference then anything. References like synthesizing and alchemy, battle strategy, and simple gameplay are easy to put in libraries without boring the player to death.
Save libraries. Keep them useful.