Often in fantasies involving magic casting spells requires a certain physical or mental toll on the caster. I don't recall any mention of spells being physically or mentally taxing in the Harry Potter universe.
Does this mean they can cast an unlimited number of spells in a given day without any negative effect to themselves?
There is definitely a canon example of spell casting exhausting the caster.
In Goblet of Fire Harry is exhausted after practicing the summoning charm a zillion times (Accio) in anticipation of the First Task.
There are other examples where some spell-specific resource limits particular spells:
the obvious is the creation of the Horcrux which, after a homicide, requires then the splitting off of part of the soul.
The casting of the Patronus Charm is contingent upon a witch or wizard being able to conjure up happy memories; several times throughout canon, Harry is unable to muster the positive energy required to produce a full corporeal Patronus. When Harry was learning the Patronus Charm in Prisoner of Azkaban, he was both mentally and physically exhausted by the experience.
Legilimens is another spell that is completely mentally exhausting, for both the caster and the recipient of the spell. It involves such mind concentration that of course it would be draining. As well, depending on what the Legilimens sees inside his/her target's head, it could be emotionally overwhelming to boot.
Learning Apparition is physically taxing and there's the risk of Splinching. When Ron Splinched in Deathly Hallows, he was quite debilitated.
In the 4th book and 4th movie, Mad Eye Moody
Or Barty Crouch disguised
taught the children the three Unforgivable Curses. He mentioned that they all take serious willpower to want to cause harm to another person as well as severe concentration to cast them successfully. He mentioned that the children probably couldn't cause more than a nosebleed if they tried to use Avada Kedavra on him.
From Goblet of Fire:
"Avada Kedavra's a curse that needs a powerful bit of magic behind it - you could all get your wands out now and point them at me and say the words, and I doubt I'd get so much as a nose bleed..."
From Order of the Pheonix:
"Never used an Unforgivable Curse before, have you boy?" [Bellatrix] yelled..."You need to mean them Potter! You need to really want to cause pain - to enjoy it - righteous anger won't hurt me for long..."
So the costs are concentration, control of magic itself, and a will to want to cast the spells. Some of these probably don't "cost" much like lumos or alohomora, but the "price" of others like the Unforgivable Curses would be considerable magic ability and emotional stress from casting them.
Yes, it means by and large, there is no limit on the ability of magic users in the Potterverse, save their ability to maintain their concentration and focus. Counter-spells and counter hexes make targeting other magic-users more difficult, but not impossible. Spells such as Protego (Order of the Phoenix) are used to prevent spells from taking effect, but are considered difficult to learn. (Half Blood Prince)
As long as a spell user has a wand, they are quite capable of performing and manipulating their environment based on their magical training and practical skill with magic. The greater natural talent, magical training and practical skill, the more effective they appear to be with magic and the more effortless they appear to be able to use said magic.
It does not mean there is no cost to the use of magic. Harry's first attempts to use the Patronus Charm to repel the boggart in the classroom with Professor Lupin (Prisoner of Azkaban) was less than successful and later only when it was backed with intense emotion was he able to create it effectively.
Rowling's writings do not seem to indicate significant stress on the part of anyone using magic except for Ron Weasley whose magical aptitude was always questionable in the early days of his education.
In the Harry Potter Universe, magic appears to function as a technology. Humans create technology in order to do work. In the Potterverse, wizards use magic to perform feats such as moving materials or themselves (Apparate or an Animagus' transformation), open doors (Alohomora), altering the composition of matter (Episkey), or altering the capabilities of people using potions (waterbreathing).
As long as the users were working with already known spells they possessed familiarity with, there seemed to be little if any physical fatigue associated with using that magic. In the early stages of magical training, there may be some fatigue until the spell becomes familiar to use.
I suspect part of the reason there is little fatigue is because of their use of wands and other foci in their spell-casting. The focus directs and supports the use of the energy of their magic, the same way a gun directs and releases the energy of a bullet from a gun.
In the same way, you could throw a rock to hit and harm an opponent, it is likely wizards could throw spells in a without a wand to attempt to disable an opponent, but the wand helps focus the magic faster, better, easier and far more effectively. I also suspect the more powerful the spell, or more powerful the effect, the greater the effort and greater the toll it takes on the spell-caster.
This explains why students might even knowing the same spell as their professors lacking the ability to defeat their far more powerful professors in direct confrontation, partially due to the students lacking the focus and concentration to effectively overcome their professors experience manipulating and controlling magical energies.
Many of the magical disciplines, such as potion-making take the effort associated with magic and places it within a potion to be released only upon consumption. So it might take you days to create a complex potion (taxing your strength and creativity until it is done) but it will sit ready once created for immediate use.
Magic acts for all intents and purposes as a means of controlling work, power and effort until such time as needed in the same manner as machines might do for the Muggles who are not part of their magical community.
The Potterverse's approach to magic use is very different from other spell using stories in which wizards or magic-users experience fatigue from their use of magic. But whether there is fatigue or not varies widely from series to series. The convention for wizards possessing limits in literature may come from their long association with role-playing games which put limits on the power of wizards such as mana use or spell use limitations to control the otherwise awesome power wizards have in that medium.
