Reb Boruch of Mezibuzh says that on Rosh Hashana we are judged on material matters, but on Shavuos we are judged on spiritual matters. (Botzina Dinehora)
It says “ad mochoras haShabbos”, meaning that we have the whole sefira including the 50th day to teshuva and purify ourselves (the word “sapir” can mean purify). And if one can’t purify himself, even on the last day, then he has no choice but to attach himself to the Tzadik Emes, and he will lift him up and purify him. Through his attachment to the Tzadik Emes, he will be able to do teshuva. (Divrei Dovid)
The Magid of Koznitz says: Before the receiving of the Torah the men were commanded in Shemos (19:15) אַל-תִּגְּשׁוּ, אֶל-אִשָּׁה – don’t come near your wives. Male is a “giver” and female is an “receiver”. The Mishana (Avos 1:3) says that we should serve Hashem without any intention of receiving reward. That’s what this alludes to; we shouldn’t be in bechinas isha, in other word an acceptor, wanting to receive reward, but should accept the Torah and fulfill the mitzvas lishma. (Avodas Yisroel)
Segulas for Children
There is a segula for one that wants a son to separate 91 perutahs on Erev Shavuos and then add more till he gets to 104, the gematria of 2 times ben, and then give it to a humble, worthy talmid chacham. (R’ Yaakov Falagi, Father of R’ Chaim Falagi)
Shevuos is a good time to daven for barren woman. It is brought down from mekubolim that when the Mishna in Roshana says that we are judged on fruits of the tree, it refers to children, because man is called a tree and the fruits are the children produced.
Tikkun Leil Shevuos
There is a custom to stay up all night on Shavuos learning Torah. The Arizal and the Shela put together an order of learning called Tikkun Leil Shevuos which many (among them Chida, Yesod Veshores Ha’Avodah and Kav HaYosher) say one should learn Shavuos night, because it accomplishes great tikkunim. The Gra used to do this also. Other’s, however, learn Gemara or other subjects with a chavrusa or listen to shiurim. Although the seforim hakedoshim emphasize the importance of saying Tikkun, it would seem that if one can’t do this that any method of learning is good.
The main thing is that one shouldn’t waste away the time. If one is going to engage in frivolous conversation then it is better to go to sleep, as the Pela Yoetz says “the sleep is good for him and good for the world”.
Arizal says that one who stays up learning Torah Shavuos Night, without wasting time, will live out the year.
It is a tikun for forbidden things one has seen with his eyes. (Pela Yoetz)
R’ Chaim Palagi says that one who awake learning Shavuos night, his Mazel will not sleep, he will clive out the year, will have sons and grandsons that are Talmidei Chachomim, is a tikin for the Shechina and is a tikun for looking at forbidden things. (Moed L’kol Chai)
The Tikun Leil Shavuos of the Rizhiner
Someone was sitting by the Tish of Reb Yisroel of Ruzhin, Shavuos night, thinking to himself that he should really be in the Beis Medrash learning Tikkun Keil Shavuos. The Rizhiner perceived what this individual was thinking with his ruach hakodesh and said the first letters of “tarich lifonei shulchon” (set before Me a table) are the same as Tikun Leil Shavuos. The man understood the message. This story could be understood through another story.
The Rizhiner ate very little, just enough to sustain him. One time, when they were reciting Birchas Hamazon, someone said to his friend that the Rebbe really isn’t allowed to bentch, because he ate less then an olive sized piece of bread. (Torah law requires one to be fully satisfied, but the Rabonon said that one should bentch on even an olive sized piece of bread.) The Rizhiner perceived the thoughts of this man and said that although the general law is that one bentches after eating an olive sized piece of bread, according to Torah law one bentches when they are satisfied on any amount of bread, and he is fully satisfied with a small piece. (I heard something very similar in the name of the Chasam Sofer.) We can see how lofty was the simple eating of the holy Rizhiner, he ate exactly what he needed, with all the proper thoughts. Now we can understand what he meant by saying that “tarich lifonei shulchon” has the same first letters as Tikun Leil Shavuos.
The mikvah of Shavuos morning (for men), shortly before Alos Hashachar, daybreak (some say 15 minutes before; some say 30 minutes before), purifies us from the seven weeks of sefira. There are great tikunim involved. It is the Mikvah of the 50th gate of binah, and of great lovingness and mercy. Mikvah saves from all troubles. (See Breslov Center's article on this and see Likutei Mohoran 56:7 for more on this.)