" Shafa'ah" (intercession) is derived from "shaf'" which means "even" as opposed to odd - the interceder adds his own recommendation to the plea of the petitioner; in this way the number of pleaders becomes even, and the weak plea of the petitioner is strengthened by the prestige of the intercessor.
Intercession on the Day of Resurrection is reserved for God and others have also been allowed to intercede with His permission. There are numerous traditions which indicate that there are many intercessors on the Day of Judgment. The intercessors include the divine prophets, religious scholars, martyrs, angels, believers, the good doers, the infallible Imams and the Quran. Only he deserves to be interceded who, in addition to God's permission, truly and constantly believes in God, the divine prophets, the Day of Resurrection and whatever God has revealed upon His prophets including the factuality and truth of intercession.
To clarify the answer to the question, it is necessary to take the following points into consideration:
1. The meaning of Shafa'ah:
" Shafa'ah" (intercession) is derived from "shaf'" which means "even" as opposed to odd - the interceder adds his own recommendation to the plea of the petitioner; in this way the number of pleaders becomes even, and the weak plea of the petitioner is strengthened by the prestige of the intercessor. 
2. The intercessors:
A) THE INTERCESSORS ACCORDING TO THE QURAN:
According to some verses of the Holy Quran, intercession is reserved for Allah.  God, the Sublime, gives the permission of intercession to whomsoever He pleases. As the knowledge of the unseen is reserved for God and God bestowed this knowledge upon His Messenger,  intercession is also reserved for God and He granted the intercessory role to His Messenger and others.
Intercession takes place in two spheres: in creation and in legislation. So far as the intercession in creation is concerned, all intermediary causes are intercessors because they are placed between the Creator and the created.
As for the intercessors in the sphere of legislation and Judgment, they may be divided into two categories: (1) intercessors in this life, and (2) those in the hereafter.
1. Intercessors in this life: All the things that bring a man nearer to Allah and make him eligible for divine forgiveness. The following come into this category: 1 - Repentance  ; 2 - True faith  ; 3 - Good deed  ; 4 – The Holy Quran  ; 5 - Any thing related to a good deed, like the mosques, holy places and auspicious days  ; 6 - The prophets and the apostles, as they seek forgiveness for their people  ; 7 – The angels  ; 8 - The believers themselves, as they seek pardon for their believing brothers and for themselves. 
2. Intercessors in the hereafter: There are many Quranic verses which denote that the intercessors on the Day of Resurrection are the prophets and the apostles  , the religious scholars, martyrs, angels  and believers.
B) THE INTERCESSORS ACCORDING TO TRADITIONS:
Many traditions have been narrated through Shia and Sunni sources in this regard. We will mention some of them as under:
1. The Messenger of Allah said: "On the Day of Resurrection, the believers approach Adam to intercede for them. They will tell him, "O Father, open the gate of Paradise for us! Adam then says: "I do not possess the merit (eligibility) to do it." They go to Ibrahim who also says, "I also do not possess the merit to do it." Prophet Moses and Jesus also say the same thing. They direct them to me. I rise up and get God's permission and help you, the Muslims, cross the Serat Bridge as fast as the speed of light." 
2. The Messenger of Allah also said: "Every Prophet has a wish to be accepted by Allah. I spared mine for the Judgment Day when I will ask the intercession for my people." 
3. Imam Ja’far ibn Muhammad as-Sadiq (as) has said, “Whoever denies three things is not our follower: The Physical Ascension; the Questioning in the Grave and the Intercession”. 
Imam Baqir (a.s.) said: "Certainly the Messenger of Allah has (authority of) intercession for his Ummah, and we have (authority of) intercession for our Shiites, and our Shiites have (authority of) intercession for their families." 
3. Who will benefit from intercession?
It is not in the best interest of religious guidance to pin-point who should benefit from intercession on the Day of Judgment. But vague hints and ambiguous statements can do no harm,  and the Qur'an has used them to give us a general idea. Allah says: "Every soul is held in pledge for what it has earned, except the people of the right hand, in gardens; they shall ask each other about the guilty: "What has brought you into hell?" They shall say: "We were not of those who prayed, and we used not to feed the poor; and we used to enter (into vain discourse) with those who entered (into vain discourse); and we use to call the Day of Judgment a lie, till death overtook us." So the intercession of intercessors shall not avail them." 
The verses declare that every soul shall remain mortgaged on the Day of Judgment for the sins it has earned, held responsible for the wrongs done in this life. They also say that the wrongdoers shall be guilty of four sins: (1) Not turning their faces towards Allah with humility and submission; (2) not spending in the way of Allah; (3) vilification - of divine revelations; and (4) calling the Day of Judgment a lie. These four evils destroy the foundation of religion. Religion demands following the purified guides, setting one's face towards Allah, turning away from the worldly distractions, setting one's eyes on the Day of Judgment. If a man succeeds in it, he will be free from the third and the fourth sins, i.e., vilification of divine revelation and calling the Day of Judgment a lie. When, in this way, his fundamental belief is secured, he shall feel the urge to turn towards Allah and to help fellow human beings. These two factors are represented in these verses by prayer and spending in the way of Allah. Faith and deed all would thus combine to build the structure of religion. Other elements, like belief in Oneness of God and the prophethood, would naturally follow. 
To make a long story short, only he is eligible for intercession who meets the following conditions:
1. True faith in God, the divine prophets, the Day of Resurrection and whatever God has revealed upon His prophets including the truth of intercession. There are verses in the Quran which explicitly state that when the unbelievers and pagans are asked: "What has brought you into hell?" They reply: "Now, then, we have none to intercede (for us)."  Therefore, the unbelievers are not eligible for intercession. In Sura Al-Anbiya verse 28 we read: "And they offer no intercession except for him whom He approves." 
Imam Reza (a.s.) was asked about the interpretation of this verse; he said: 'It means acceptability in matters of faith." Hence, intercession is for sinners provided that they are approved in terms of faith and belief. The obstinate ones, the Nasibis (enemies of Ahlul-Bayt) and deniers are deprived of intercession.
2. Those who do not believe in Shafa'ah will be deprived of it. The Messenger of Allah, peace be upon him and his family, said: "And whoever does not believe in my intercession, may Allah not extend to him my intercession." 
3 & 4. Intercession is for those who establish prayers and help the needy. As stated in Sura-e Muddathir,  the reason many criminals go to hell is because they abandon prayers, do not help the needy and deny the Day of Judgment. Imam Sadiq (a.s.) said: “Our intercession is not for those who consider the Prayers unimportant.” 
In any case, intercession is not an absolute and unconditional subject. In fact, it features certain conditions and limits about the sins and crimes as well as the intercessors and those who are interceded. Those who believe in this principle and who wish to avail themselves of this opportunity so as to be among those who are interceded should meet the conditions by staying away from sins and shirk etc. that are not included in the intercession or they should behave in a way such that should draw the attention of the intercessors.
For further information see the following indexes:
4. Index: Dispossession of benefit and harm from the Prophet (s) and seeking intercession and cure from him, question 84 (site: 2378).
 - Tabatabai, Muhammad Hussein, Tafsir Al-Mizan, vol.1, pg. 157.
 - Al-Baqarah, 256; Al-Zumar, 44.
 - Jinn, 27.
 - Al-Zumar, 54
 - Al-Hadid, 28
 - Al-Maedah, 9.
 - Al-Maedah, 16.
 - An-Nisa, 64.
 - Ibid
 - Al-Momeen, 7.
 - Al-Baqarah, 286.
 - Al-Anbiya, 28
 - Zukhruf, 86
 - Behar al-Anwar, vol.8, pg. 35.
 - Shaykh Mufid al-Ikhtesas, pg. 37
 - "مَنْ أَنْکَرَ ثَلَاثَةَ أَشْیَاءَ فَلَیْسَ مِنْ شِیعَتِنَا الْمِعْرَاجَ وَ الْمُسَاءَلَةَ فِی الْقَبْرِ وَ الشَّفَاعَةَ". . Behar al-Anwar, vol.6, pg. 223.
 - Ibid, pg. 48.
 - Al-Mizan, vol.1, pg. 159.
 - Al-Muddathir, 38-48
."کُلُّ نَفْسٍ بِما کَسَبَتْ رَهِینَةٌ، إِلَّا أَصْحابَ الْیَمِینِ، فِی جَنَّاتٍ یَتَساءَلُونَ، عَنِ الْمُجْرِمِینَ ما سَلَکَکُمْ فِی سَقَرَ؟ قالُوا: لَمْ نَکُ مِنَ الْمُصَلِّینَ، وَ لَمْ نَکُ نُطْعِمُ الْمِسْکِینَ، وَ کُنَّا نَخُوضُ مَعَ الْخائِضِینَ، وَ کُنَّا نُکَذِّبُ بِیَوْمِ الدِّینِ، حَتَّى أَتانَا الْیَقِینُ، فَما تَنْفَعُهُمْ شَفاعَةُ الشَّافِعِینَ"
 - Tafsir al-Mizan, translation, vol.1, pg. 259.
 - Shu'ara: 100
 - "و لایشفعون الا لمن ارتضی".
 - "مَنْ لَمْ یُؤْمِنْ بِشَفَاعَتِی فَلَا أَنَالَهُ اللَّهُ شَفَاعَتِی". Behar al-Anwar, vol.8, pg. 34.
 - See verses 40 – 48.
 - "إِنَّ شَفَاعَتَنَا لَا تَنَالُ مُسْتَخِفّاً بِالصَّلَاةِ". Wasail al-Shia, vol.4, pg. 25.