Our group had some confusion about preparing spells for a Wizard and Cleric. The rules say that you prepare a number of spells from your list and that you tick off spell slots when you cast a spell. In D&D 3.x, if you wanted to cast a spell multiple times you had to prepare it multiple times, but we couldn't figure out from the rules whether or not this was the case in D&D 5e.
So can a spell be prepared once and then cast multiple times?
From the D&D Basic Rules (e.g. from the cleric's or the wizard's Spellcasting feature):
Casting the spell doesn't remove it from your list of prepared spells.
Basically, 5e Wizards (and Clerics) are 3.5e Sorcerers who can swap out their "known spells" based on their spellbook (or godly mandate).
I can't speak to the exact reason behind the design decision, but I assume they wanted to enable a level of flexibility for both classes that was often lacking in previous editions.
Yes. Preparation doesn't mean the same as it does in 3.x; this is a case where knowledge of prior editions is an impediment to understanding D&D 5E.
Preparation in D&D 5E is a separate pool of capability from casting capability, and is not undone by casting the spell.
Page 78 of D&D 5E Basic Rules (Bolding mine for emphasis):
Known and Prepared Spells
Before a spellcaster can use a spell, he or she must have the spell firmly fixed in mind, or must have access to the spell in a magic item. Members of a few classes have a limited list of spells they know that are always fixed in mind. The same thing is true of many magicusing monsters. Other spellcasters, such as clerics and wizards, undergo a process of preparing spells. This process varies for different classes, as detailed in their descriptions.
In every case, the number of spells a caster can have fixed in mind at any given time depends on the character’s level.
Spell Slots
Regardless of how many spells a caster knows or prepares, he or she can cast only a limited number of spells before resting. Manipulating the fabric of magic and channeling its energy into even a simple spell is physically and mentally taxing, and higher level spells are even more so. Thus, each spellcasting class’s description includes a table showing how many spell slots of each spell level a character can use at each character level. For example, the 3rd-level wizard Umara has four 1st-level spell slots and two 2nd-level slots.
When a character casts a spell, he or she expends a slot of that spell’s level or higher, effectively “filling” a slot with the spell. You can think of a spell slot as a groove of a certain size—small for a 1st-level slot, larger for a spell of higher level. A 1st-level spell fits into a slot of any size, but a 9th-level spell fits only in a 9th-level slot. So when Umara casts magic missile, a 1st-level spell, she spends one of her four 1st-level slots and has three remaining.
Finishing a long rest restores any expended spell slots (see chapter 8 for the rules on resting).
Some characters and monsters have special abilities that let them cast spells without using spell slots.
The header levels for both chunks are the same - so it's implied strongly to be two separate rules.
So, we have a mention that each class has a rule limiting prepared spells. The actual limit is mentioned in each class's special rules. Level plus attribute modifier is the limit for both Cleric and Wizard. (See pp. 22 & 30.)
Note that it's possible for a 1st level wizard to cast 2 spells per day of level 1 (see pp. 29); if he's INT 18, he can have up to 5 prepared (INT 18 is a +4 modifier, and so level + Int Mod is 5). Likewise, a wizard of INT 9 or lower can prepare no spells at 1st level; he can only use his cantrips. So his slots will be unused. (An INT 8-9 Wizard can prepare a single spell at 2nd level; an INT 6-7 Wizard has to hit 3rd level to prepare one spell, but that spell can be a 1st or 2nd spell level.
Also note that ritual use requires neither preparation nor a spell slot, so the idea of a low-Int Wizard isn't the non-sequitur it may at first seem.
Note that prior editions all clearly stated that casting erased the prepared spell from the caster's mind or that the spell had to be prepared multiple times to use it with multiple spots.
Note that the D&D 5E Wizard (and Cleric) are actually closer in mode to the 3.X Sorcerer, than the 3.X Wizard.
Yes, both the Cleric and the Wizard can use a prepared spell multiple times as long as she or he has expendable spell slots for it.
Both classes' "Preparing and Casting Spells" section explicitly states that casting a spell does not remove it from your character's list of prepared spells.
For characters that prepare spells:
Prepared spells are the spells that a character knows how to cast. These stay prepared until the next time a character prepares their spells, regardless of how many spell slots the character has left. Normally they can only prepare spells after a long rest has been done since the last time they prepared spells.
Spell slots are how many spells a character can cast. These are used up as the character casts spells and are all regained after a long rest.
