(1) Accomplishing Moksh.
(2) Accomplishing prosperity.
(3) Attaining the goal. Or fulfillment of Disciple's desire
(4) Attaining power.
(5) Siddhi means success. It includes accomplishment, achievement, success and fruition of all kinds. A person may thus gain Siddhi in speech, Siddhi in Mantra etc.

In our Religion, there are 33 crore Devtaa and all of them have a separate Mantra for them. Vishwaamitra Jee did Upadesh of all these Mantra to Raam. Vishwaamitra Jee had done Lakhs of Jap of all these Mantra, performed "Purascharan", relevant Hom, "Sandarpanai" and then saw each of these Devtaa directly. After the performance of thousands of years of Jap, Vishwaamitra Jee saw each of these Dev. So what is the "Siddhi" of a Mantra? "Siddhi" means to directly see the Devtaa of the Mantra.

When Vishwaamitra Jee taught all these Mantra to Raam. Before Raam could utter them even once, the relevant Devataa rushed up to His Presence. One by one all Devtaa rushed to his side. None desired to leave the presence of Raam. So, Raam absorbed each one of them in His own "Shareer" (body). In the same way while chanting the Gayatri Mantra we do its "Aavaahan" (installation or invocation) within ourselves. We do "Aavaahan" in water or fire. When Ganapati Hom is performed, the god is installed in the fire lit for the Hom. It is into this that Fire that we offer 'Kozhukattai' (a sweet dish that is the favorite of Lord Ganesh), sugarcane, etc. When the "Aavahaan" is done into water, we pour the holy water on to our head after the completion of worship.

There is yet another type of "Aavaahan". This is to do "Aavaahan" on ourselves. This is done while doing "Sandhyaa Vandan". Thus, where did all the 33 crore Devtaa go to? They are verily within Raam's "Shareer". Thus, one who chants Raam Mantra receives the "Phal" of chanting Mantra of all gods and one who worships Raam receives the "Phal" of worshipping all Dev. For whom does the above apply? It is for one who wishes to know the "Tattwa" of Raam. But, if one acquires "Ruchi" (taste) for "Shree Raam Jaya Raam Jaya Jaya Raam", we would not wonder, why should we chant this? Which god's Naam is this? What is the "Phal" for chanting this? This is because mere chanting the Naam itself gives us joy.
We should develop a taste for the Naam of Bhagavaan. We should feel sad if questions arise in us because it goes to show that we have not developed Bhagavaan Naam Ruchi.

Why question, "Whose name is this? How many times should I do this Jap? What is its glory? What is its "Tattwa" (philosophy)?" All such details are needed only by one who has no taste for Naam. Bhagavaan will not speak to one who has no "Ruchi" in His name; such a person will not attain "Naam Siddhi" too. "Ruchi" usually comes through Guru Kripaa or Daiv Kripaa (Grace). Once we get the taste of the Naam and do Jap of it, it can do wonders. We see that Raamdaas Jee had performed Jap of "Shree Raam Jaya Raam Jaya Jaya Raam".

Understanding Siddhi
There are 2 main things when it comes to Mantra Tantra Saadhanaa - one is Siddhi of that Mantra or Devee / Devtaa / Isht where the concerned Devee or Devtaa or Deity shows up itself in front of you, this is called Pratyaksheekaran. This is the Siddhi level which is a high level and is a long process depending on what Saadhanaa you are doing. Once this is accomplished you are called a Siddh Purush. For any Siddhi you will need to take many Charan of Shaktipat Deekshaa related to that Saadhanaa. The other aspect is small or big Mantra Saadhanaa Prayog that we do for solving our temporary problems or issues for the present time being. Saadhanaa Prayog are also done for specific wish-fulfillment. Now one needs to understand that you may or may not get results from your Saadhanaa Prayog the 1st time, if you do not get the desired results then you may have to repeat the Saadhana Prayog again & again until you get the desired result. Again Shaktipat Deekshaa is needed for everything after discussing with Guru. For some simple Mantra Prayog you may not need any Shaktipat Deekshaa. Always do 4 Maalaa of Guru Mantra Jap before doing any Saadhanaa. Now if you get the desired results from your Saadhanaa Prayog it does not mean you have got some Siddhi, what you have done now only solved your temporary problem or issue or fulfilled your wish for the time being. Riddhi Siddhi is a totally different level. These are two different things that one needs to understand.

Types of Siddhi (Powers)
In Bhaagvat Puraan, 11/12, Krishn says - There are 18 types of Siddhi, among them eight types of Siddhi are the top most powers and they are with Bhagavaan Himself. They are - 
(1) Animaa - Ability to shrink one's material to atomic size as desired, Through this Siddhi one may enter into stone or change the density in one's body, enabling one to pass through solid matter.
(2) Mahimaa - To expand one's material body to a gigantic size, ultimately enveloping the universe.
(3) Laghimaa - To become light and invisible as air, and fly at will. The perfection of this Siddhi enables one to travel on the Sun's rays and enter into the Sun planet.
(4) Praapti - Ability to manifest any thing in one's hand. This Siddhi removes the limitations of space which separate two objects from each other. It is said one will even be able to touch the Moon with one's finger [ie the limitation of distance is removed]. In fact this sequence is the natural sequence of manifestation of gross matter. The Praapti Siddhi enables one, through Mantra, to reverse the process and transform gross physical objects into ethereal objects by merging the respective elements into their source element. Thus one takes an object located in a particular location, and by utilizing Mantra Siddhi, one merges the Earth element into the Water element, the Water element into the Fire element, the Fire element into the Air element, and finally the Air element into the Ether element. As you merge each element into the previous, element, the corresponding quality disappears (being merged back into the source element). In this way, a physical object is transformed into an Ethereal object with no quality other than sound - because Ether is the first element and its subtle quality is only sound. Thus this ethereal object can be transferred over space by mind, and then the entire process is reversed to re-manifest the original object in one's hand.
(5) Praakaamya - To witness or enjoy all pleasures in the Three-worlds,
(6) Eeshitaa - The power to gain control over the sub-potencies of the laws of nature. This enables one to control various energies and seemingly defy the laws of nature. On the lowest level, one may make fire come from one's mouth, etc.
(7) Vashitaa - Non-attachment to enjoyments, or to gain control over others.
(8) Kaamaavasaayitaa - To attain freedom from all desires. The ability to attain anything anywhere. This is the highest of the eight Siddhi and contains most of the abilities of the other perfections.

The other 10 Siddhi (secondary perfections) can be developed by following Sato Gunee behavior. And the rest of the Siddhi can be achieved only by Yog.

Among these eight Siddhi, which are with Bhagavaan Himself, the first three belong to the body. The 4th one, Praapti belongs to Indriyaan. Praakaamya Siddhi can make one experience worldly and Divine materials according to one's desire. To manage Maayaa and its functions according to one's wish is Eeshitaa. Not to be attached with pleasures, in spite of living amidst pleasures, is called Vashitaa. One desires whatever pleasure, attaining it completely is called Kaamvasaayitaa Siddhi. These eight Siddhi are with Bhagavaan naturally, and to whomever He gives them, He gives them only partly.

Those other 10 Siddhi are, for example,
(1) control over hunger and thirst; With this perfection one no longer depends on food and water for maintenance of one's body. One will be able to sustain himself simply on Praan, the life air.
(2) seeing the things at a very far distance; With this perfection one develops a mystic vision, by which one can see any person or place. Sanjaya, the charioteer of Dhritraashtra, used this Siddhi to see and hear the conversation between Krishn and Arjun (known as Bhagvad Geetaa) which took place on the battlefield of Kurukshetra, though he was situated far away.
(3) hearing something from a very far distance; With this perfection one can hear any conversation spoken anywhere in the world.
(4) appearing at some place with mind and body; With this perfection one can travel great distances in a moment simply by thinking of the destination.
(5) assuming any form according to one's desire;
(6) entering in other's body; This perfection enables one to enter into the bodies of others and enjoy through their senses. Since ghosts do not have physical senses, they often resort to this to satisfy their desires through other's bodies.
(7) leaving the body whenever one wishes. The ability to control the time of one's death. With this perfection one may choose the time of leaving his body.
(8) to see Devtaa's play with Apsaraa;
(9) Siddhi of Sankalp or Satya Sankalp - Perfect accomplishment of one's determination. Whatever one desires to happen will happen;  and
(10) making all obey to himself without any hesitation.

These 10 Siddhi can be attained by developing Sat Gun.

And the following five Siddhi can be attained by a Yogee. They are called five inferior Siddhi --