Relatives are those who are related to you through blood and close-ties; such as the brother, the uncle, the aunt, or their children. Everyone who has a tie of relation with you has certain rights upon you, in accordance with how closely they are related to you. About this, Allaah - the Most High - said:
"And give to the relative his right." [Soorah al-Israa' 17:26]
Allaah - the most high - also said:
"And worship Allaah alone, and do not set-up any partner to Him in worship,
and be kind and good to the parents, and to the relatives." [Soorah an-Nisaa 4:36]
So it is obligatory upon everyone to treat their relatives in the best possible manner, and to support them in accordance with their needs, and what they seek of help and support. And this is what is necessitated by the Sharee'ah (Prescribed Islaamic law), the 'aql (sound reasoning) and the fitrah (natural state).
And there are many textual evidences encouraging and silatur-raheem (joining the ties of relations); such as what Aboo Hurayrah radiyallaahu 'anhu relates from the Prophet (sallallaahu 'alayhi wa sallam), that he said "Indeed Allaah created the creation, until he was finished doing so, the Rahm: (womb/ties of relation) stood-up and said: Is this the place of one who seeks refuge in you from those who severe and cut ties with me. So Allaah said: Yes, Indeed Would it please you that I keep ties with those who keep ties with you, and cut-off ties with those who cut-off lies with you? So the Rahm': said: Yes, indeed' So Allaah said: Then this is for you. Then Allaah's Messenger (sallallaahu 'alayhi wa sallam) said: "Recite if you wish: "Would you then, if you were given the authority, cause corruption in the land, and cut-off lies of relations. They are those upon whom is the curse of Allaah, so that He makes them deaf and blinds them." [Soorah Muhammad 47:22-23] 
The Prophet sallallaahu 'alayhi wa sallam also said: "Whosoever believes in Allaah and the Last Day let him keep the ties of relations." 
Unfortunately, many people do not fulfil this haqq (right) and transgress the bounds concerning this. Some of them do not seek to join ties with relatives or show kindness to them; neither through wealth, nor through good behavior, nor through the giving of occasional gifts and presents, nor through rendering help to them in their times of need. Indeed, many days or months may pass without even seeing or visiting them. And sometimes, rather than seeking to join ties of relations, some people even intend to severe such ties, by seeking to harm their relatives - either through words, or action, or both. Such people only even keep close lies with those who are not relation, yet cut-off ties with relatives!Some people only keep ties of relations with those who maintain ties with them, but cut off from those who cut off from them. So such people are not truly the waasils (those who keeps ties of relations), but rather they are those who do so based upon tit for tit. So they will only keep ties with those who keep ties with them -whether relatives, or other than them. However, the true waasil (one who keeps ties of relations) is the one who keeps ties of relation for the sake of Allaah - regardless of whether his relations keep ties with him or not.
'Abdullaah Ibn 'Amr (radiyallaahu 'anhu) relates that the Prophet sallallaahu 'alayhi wa sallam said: "The waaasil (one who keeps the ties of relations) is not the one who merely does so out of reciprocation. Rather, the waasil is the one who, even when the relatives cut-off him, yet he still maintains ties with them." So a man asked: O Messenger of Allaah, I have relatives with whom I maintain ties of relations, yet they cut-off from me. I treat them kindly, yet they treat me in an evil manner. And I am forbearing and patient with them, yet they behave rudely and ignorantly towards me. The Prophet (sallallaahu 'alayhi wa sallam) said:
"If the situation is as you say, then it is as if you are filling their mouths with sand. And Allaah will continue to aid and support you as long as you continue doing what you are doing." 
If there were no other rewards for keeping ties of relations, except that Allaah keeps ties with the waasil in this world and the hereafter, and that He extends his Mercy due to it, and makes affairs easier through it, and removes distress and anxieties by it, then that would be more than sufficient. However, along with this, silatur-Raheem (joining the ties of relations) brings with it closeness to one's family and relatives, as well as love and compassion developing between one another, and their being mutual help, in times of ease and hardship, between one another, and other such joys and delights - as is experienced and well-known. And when ties of relations are not maintained, then each one of the aforementioned benefits turns into their opposites, and great harm comes to the society.
1. From Huqooq Da'at Ilayhal-Fitrah wa Qarrathash-Sharee'ah (pg.11-13) of Shaykh Muhammad Ibn Saalih al-'Uthaymeen.
2. Related by al-Bukhaaree (no.5987) and Muslim (no.3456).
3. Related by al-Bukhaaree (no.6138), from Aboo Hurayrah (radiyallaahu 'anhu)
4. Related by al-Bukhaaree (no.5991)