In previous versions, spell casters were given bonuses to available spells based on their casting ability score. I don't remember exact stats but to make an example, A wizard would be able to memorize extra spells:
Int 14 = 1 extra lvl 1
Int 15 = 2 extra LVL 1
Int 16 = 2 extra lvl 1 and 1 extra lvl 2
Int 17 = 2 extra lvl 1, 2 extra lvl 2 and is required for casting lvl 8 spells
Int 18 = 2 extra lvl 1, 2 extra lvl 2, 1 extra lvl 3, and is required for casting lvl 9 spells.
I can't seem to find mention of this bonus in D&D 5th Edition. Does it apply to prepared spell limit, spell slots, or has it been obsoleted?
Note: I also can't seem to find mention of a prepared spell limit, or feats.
There is no such bonus for spells known
Wizards learn their spell on level up or through transcribing them into a spellbook, but their ability score does not have an effect on how many they can learn or do learn on level up.
For classes that only get spells through level up or are prepared casters, the number of spells known can be found in the table for those classes in the Player's Handbook. The number that can be prepare can be found in the class descriptions usually in a section called "Preparing and Casting Spells". Preparing spells does actually usually depend on the spellcasting stat.
For example for cleric it says: