Dungeon Master: Known Spells

The number of known spells affects the strength of a spellcaster. However, outside the wizard, most classes can't learn more spells outside of their leveling. The wizard, however, can learn many new spells (through finding spell books and spell scrolls) and become a utility powerhouse due to their wide range of options. I'll try to talk about ways to bridge the gap for other classes as well as some problem that may result.

Possible Problems

Wizards are limited in the number of spells they can prepare. This means that even though they have many options, they have to make a choice. Other classes, however, always bring everything they know to the table. This means that if you decide to give every arcane spell possible to a sorcerer, they will not be limited by the preparation rules of a wizard and become even more well-rounded. If all you have in your campaign is a sorcerer, it may not be too much of a problem since the party wizard won't feel overshadowed. Otherwise, if done, it needs to be limited and done carefully to prevent the situation I mentioned.

Learn by Watching

You can decide that you want your sorcerers to learn new spells from watching others cast the spells. Clearly this is harder and more time consuming than passing around and mass producing books. It also, from a gameplay perspective, adds another reason for your sorcerer to pay attention. It also feels awesome to learn a new spell and pull it out to save everyone in the middle of combat (person experience talking). You need to trust your player, however, since keeping track of this in combat is very difficult. Whenever I've seen Dungeon Masters use a system like this, they would trust the player and not keep track themselves.

More Spells Are Needed

Just giving spells to the players that are important for riddles or other reasons is another solution to the problem. There are also some spells that are mathematically awesome that people always gravitate towards. If you give these for free and let them take other ones, the result is a character that can do cool things outside of combat as well as within it. However, again, some spells can make it easy for magic characters to completely overshadow the rest of the party. As a result, serious care should to be taken or other benefits should to be given to the non-magic characters in order to offset the result.

Spell scrolls can also be made available to these characters. It's an easy way to give access to tons of spells that the players may not otherwise have access to. Copying the spells from the spell scrolls is also not a problem for the non-wizard magic classes I was talking about so they are far less dangerous for a campaign in their hands.

Just Don't Give Many Spells to the Wizard

There is also a very easy solution to the problem from the start. If you don't give your wizard every spell under the sun, the entire problem goes away. A few spells here and there won't unbalance things too badly though.

Taking Away Spells

Spells like wish, which can be taken away from the player, can be a big problem for classes that cannot learn more spells as written. In these cases, you might choose to be merciful and let the player take a different high level spell to take its place. However, if your campaign features situations where spells or knowledge about spells is taken from players more often, beware that it will affect those other classes far more widely than the wizard (assuming the wizard has access to spell books and spell scrolls).