What are the types of jutsus that exist in Naruto?

Question

There seem to be a number of different types of jutsus that exist in Naruto. These include ninjutsu, taijutsu, and genjutsu. What are all of the types of jutsus and what do they do?

Answer 1

^{DISCLAIMER: I've never seen or read anything Naruto.}

This questions seems rather simple to me, so perhaps you're looking for a specific angle? There is a good ammount of info on Jutsu on Narutopedia. Here I will try to quote that article in brief summaries.

What is Jutsu?

Jutsu ... are the mystical arts a ninja will utilise in battle. To use a technique, the ninja will need to use their chakra. To perform a technique, the ninja will bring out and release the two energies of chakra. By forming hand seals, the ninja is able to manifest the desired technique. Because of the extensive number of hand seals and different combinations, there are thousands of potential techniques to be discovered. -- Jutsu, Narutopedia

What are the different types of Jutsu?

There are three principal types of jutsu:

• Ninjutsu ...a term referring to almost any technique which allows the user to do something that they otherwise would be incapable of doing, including the usage of weapons.
  More info: Ninjutsu, Narutopedia
• Genjutsu are techniques that are employed in the same fashion as ninjutsu... However, the primary difference between the two is that the effects of genjutsu are illusory; instead of attacking the victim's body, like taijutsu or ninjutsu, genjutsu techniques manipulate the flow of chakra in the victim's brain, thus causing a disruption in their senses.
  More info: Genjutsu, Narutopedia
• Taijutsu a basic form of techniques ... refers to any techniques involving the martial arts or the optimisation of natural human abilities. Taijutsu is executed by directly accessing the user's physical and mental energies, relying on the stamina and strength gained through training. It typically does not require chakra, though chakra may be used to enhance its techniques. Taijutsu generally requires no hand seals to perform, occasionally making use of certain stances or poses, and are much quicker to use than ninjutsu or genjutsu. Taijutsu is simply put: hand-to-hand combat.
  More info: Taijutsu, Narutopedia

-- Jutsu, Narutopedia

There are several sub-types including:

• Barrier Ninjutsu ...the incorporation of barriers into techniques.
• Bukijutsu ...techniques that entail the use of any handheld weapons in combat, whether the users be shinobi or samurai.
• Chakra Absorption Techniques ...techniques that allow the user to absorb another individual's chakra.
• Chakra Flow ...the flowing of chakra through an object as well as any technique that increases the potency of a weapon by flowing chakra through it..
• Clone Techniques ...techniques that create a copy of the user or objects used by them.
• Collaboration Techniques ...techniques which entails powerful techniques that are actually comprised of at least two or more pre-existing techniques.
• Fūinjutsu ...a type of jutsu that seal objects, living beings, chakra, along with a wide variety of other things within another object.
• Hiden ...techniques are passed down orally from generation to generation in certain regions or clans.
• Juinjutsu ...techniques used to bring someone under the control of the user.
• Kenjutsu ...techniques that entail the use of swords, whether the users be shinobi or samurai.
• Kinjutsu ...techniques that have been banned from being taught or used.
• Medical Ninjutsu ...a branch of ninjutsu associated with healing...
• Nintaijutsu ...a combination of ninjutsu and taijutsu, the Raikage uses nintaijutsu by first surrounding himself with his Lightning Release Armour.
• Reincarnation Ninjutsu ...techniques that usually require or accomplish the transfer of life force between people.
• Senjutsu ...a specialised field of techniques that allows the user to sense and then gather the natural energy ... around a person.
• Shurikenjutsu ...techniques that entail the throwing of shuriken, kunai, senbon or any other of a number of bladed, hand-held weapons.
• Space–Time Ninjutsu ...techniques that allow the users to manipulate the space–time continuum.
• Tailed Beast Skill a unique ability or trait used by tailed beasts.

-- Jutsu, Narutopedia

I hoped this helped! :)

Answer 2

There are three main types of jutsu:

• ninjutsu, the ability to do things one otherwise could not. (Usage of weapons, etc.)
• genjutsu, an ability requiring chakra and hand seals, used to perform an illusion on an enemy in order to trick them or disrupt their senses.
• taijutsu, abilities governed by learnable techniques such as martial arts and using the physical and mental energy of the body.

There are also several more "sub-jutsu" that are basically subsets or subcategories of the three above:

• barrier ninjutsu, the use of barriers for protection, trapping an enemy, and so on.
• bukijutsu, the use of handheld weapons in combat, such as (but not limited to) shuriken.
• chakra absorption techniques, the ability to absorb another's (usually an opponent's) chakra.
• chakra flow, the use of chakra flow through objects such as weapons.
• clone techniques, the use of clones (either of the user or of weapons/objects he may have), generally for purposes of distraction.
• collaboration techniques, the use of two or more techniques (usually by multiple users) to combine chakra into a greater power.
• fūinjutsu, techniques used to either seal or unseal objects, opponents, chakra, and so on.
• hiden, techniques which are not of a specific type but rather are those passed secretly between generations in specific regions or clans.
• juinjutsu, the use of cursed seals to take over another's body.
• kenjutsu, the use of swords. (Often combined with other jutsu.)
• kinjutsu, banned techniques.
• medical ninjutsu, techniques used to heal one's own, or another's, body.
• nintaijutsu, the combination of ninjutsu and taijutsu used by the third and fourth Raikage.
• reincarnation ninjutsu, techniques used to transfer life force between subjects. (Similar, but not the same as, kinjutsu.)
• senjutsu, the use of the energy in nature with one's own chakra for much greater (and varied) effect.
• shurikenjutsu, the throwing of bladed hand-held weapons.
• space–time ninjutsu, techniques which warp space–time; this allows, for example, teleportation between locations.
• tailed beast skill, any technique used by a tailed beast.

This is a fairly extensive list, but you can take a look at the reference list which also lists something called "blood limit types", which are inherited rather than learned.