Hugging and kissing relatives:
It is forbidden to hug or kiss any of one’s relatives, including one’s adult sister or aunt [and uncle, niece, nephew, cousins] and the like, with exception to a father/mother and daughter/son, as will be explained. This prohibition applies even though there is naturally no physical attraction towards the relative and one receives absolutely no pleasure at all from the act of hugging or kissing. Hugging or kissing such relatives is a most deplorable act, and is an act of prohibition, and is the doings of a foolish person, as one is not to bring himself in physical closeness with any relative of the opposite gender, whether she is an adult or a child.
Parents, Grandparents, children and grandchildren: Kissing and hugging is permitted between parents and children even if they are of the opposite gender [and even if the children are now adults]. Thus, a mother may hug and kiss her son [of any age] and a father may hug and kiss his daughter [of any age]. [See Q&A regarding if she is married!] Kissing and hugging is likewise permitted between grandparents and grandchildren of the opposite gender.
Brother/sister and other relatives who are still children: See Halacha 3!
May a parent/grandparent hug a married daughter/granddaughter?
Some Poskim rule it is permitted for a father or grandfather to hug and kiss his daughter/granddaughter even if she is married. Other Poskim however rule it is forbidden for them to kiss or hug a married daughter/granddaughter. Practically, it is permitted to do so, although one who desires to be stringent upon himself is blessed.
May one shake hands with his/her sister/brother?
 Michaber Even Haezer 21:7; Rambam Issureiy Biyah 21:6; Shabbos 13a “Ula stated that any closeness is forbidden as we say to the Nazir Sechor Sechor…”; Avoda Zara 17a; Bach in Kuntrus Achron 21; Meil Tzedaka 19; Chochmas Adam 125:1; Igros Moshe Y.D. 2:137; Nitei Gavriel Yichud 53:1
The law by a Tzaddik: Although Ula himself made the above statement prohibiting any physical engagement between relatives, Ula himself would kiss his sisters by the hand or by the chest [Bei Chadaihu]. [Shabbos ibid] This is because Ula was a complete Tzaddik, and knew that he would not be led to any immoral thoughts. [Chelkas Mechokek 21:8; Beis Shmuel 21:14; Tosafus Shabbos 13a; See Meil Tzedak 19] Likewise, Ula would not come to do so with any other women, as he was a complete Tzaddik, and hence there is no reason to decree against him kissing his sister. Other people however may learn to hug other women if this were to be allowed. [Igros Moshe ibid] Another example of the above allowance for Tzadikim can be found in scripture where Yaakov kissed Rachel. [See Meil Tzedaka 19; Od Yosef Chaiy Parshas Shoftim p. 151]
Other opinions: Some Poskim imply that there is never a prohibition to hug and kiss a relative [even of permissible marriage] if one is doing so without any sexual intent or pleasure, and is merely done out of Derech Eretz and the way of the world. [Meil Tzedaka ibid in his answer of Ula; Od Yosef Chaiy Parshas Shoftim p. 151 based on Midrash Raba Vayeitzei and on Heter for a male doctor to have a female patient.]
 The Michaber ibid states one’s father’s sister, although obviously the same would apply to one’s mother’s sister.
 See Chochmas Adam ibid for a list of all the Arayos
 Is this a Biblical or Rabbinical prohibition: Hugging, kissing, and other touch of relatives which is done for the sake of sexual pleasure, or from which one receives sexual pleasure, is a complete Biblical prohibition which is liable for lashes and is to be protested against. [Bach in Kuntrus Achron 21] Thus, hugging and kissing relatives which one can marry, such as a niece, or cousin, is a complete Biblical prohibition which is liable for lashes and is to be protested against. The reason for this is because one has benefit and pleasure from such contact, and is therefore include in the Biblical prohibition of touching an Erva in a form of Chiba [affection]. It is therefore Rabbinically forbidden even for a Tzaddik to hug and kiss such relatives, even though he has absolutely no erotic thoughts, as this appears as a forbidden act of affection. However, hugging and kissing other relatives in which marriage is forbidden, and there is no natural attraction to them, such as a sister and aunt, is only a Rabbinical prohibition due to a decree that one may come to do so with other relatives. However, there is no Biblical prohibition involved being that the Biblical prohibition only applies if one does so “Derech Chiba” in a way of pleasure. One is therefore not required to protest against one who does so, if one assumes that they will not listen. [Igros Moshe ibid] See Beis Shmuel 21:14 that uses the term “forbidden” and not just a Davar Issur as writes Michaber; See Otzer Haposkim 21:51 in name of Batei Kehuna
 Michaber ibid; Kiddushin 80b; Kitzur SHU”A 159:10
 Perisha 21:7; Beis Shmuel 21:15; Beir Heiytiv 21:15; Taharas Yisrael 21:17; Chochmas Adam 125:6
The daughter/granddaughter/mother/grandmother is a Nida: The above allowance applies even if the relation is a Nidah. [Betzeil Hachochmah 3:12]
 Chelkas Mechokek 21:10 based on Kiddushin 81b; Beis Shmuel 21:14 [see there for a long discussion on this topic]; Pischeiy Teshuvah 21:5; Igros Moshe ibid
 Beis Shmuel 21:14 that when both are clothed there is no prohibition to sleep together even if she is an adult and is married; Pnei Moshe 21:5; Beir Heiytiv 21:14; Aruch Hashulchan 21:10; Taharas Yisrael 21:17; Nidchei Yisrael 24; Divrei Yatziv Even Haezer 36; Chochmas Adam 125:6 concludes with a Tzaruch Iyun; Betzeil Hachochmah 3:12
 Mishneh Lamelch on Rambam 21:6-7; Nesivos Shabbos 13a; Meiri Kiddushin 81b; See Betzeil Hachochmah ibid
 Betzeil Hachochmah 3:12 as rule majority of Poskim ibid
 Betzeil Hachochmah ibid; Beir Moshe 4:145; Igros Moshe Even Haezer 1:60 and 4:63; See also Od Yosef Chaiy Shoftim 21 that a Baal Nefesh is to be stringent to himself. [does not specifically stipulate regarding daughter that is married].
 Rav Elyashiv in Koveitz Teshuvos 2:20; Mishneh Halachos 4:186
 The reason: As the Sages only forbade clear acts of affection, such as hugging and kissing, and not acts of respect such as shaking hands.