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Women are exempt from all time bound positive commandments (Mitzot Aseh Shehazman Grama) with a few exceptions, which will be listed below. 
If a women wants to do a Mitzvah that she is exempt from she is permitted and encouraged to do so. Ashkenazim hold that women can make a bracha on such mitzvot even though they are exempt, while Sephardim hold that women can't make a bracha since they are exempt. 
Tzitzit is a Mitzvah Aseh SheHaZman Grama and so women are exempt.  Even though usually women are allowed to fulfill מצות from which they are exempt, by Tzitzit it’s preferable that women do not fulfill this mitzvah. 
Tefillin is a Mitzvah Aseh SheHaZman Grama and so women are exempt. Even though usually women are allowed to fulfill מצות from which they are exempt, by Tefillin it’s preferable that women do not fulfill this mitzvah. 
Tefilla is a Mitzvah Aseh SheHaZman Grama but nonetheless women are obligated in praying once a day and it’s praiseworthy to pray three times a day.  There is a dispute regarding Mussaf; see further Sh”t Yabia Omer 2:6(7).
Regarding the mitzvah of saying one hundred Brachot each day some consider it a Mitzvah Aseh SheZman Grama, while others disagree. 
Women are obligated in Kiddush on Shabbat. Even though Kiddish is a time bound positive mitzvah women are obligated because there is a comparison between Shamor and Zachar and since women are obligated to keep the negitive commandments of Shabbat so too they're obligated in the positive mitzvot of Shabbat. 
Some say that there’s an obligation of women to hear Kriyat HaTorah but the minhag is to lenient in this regard. 
Women are obligated to eat Matza on the first night of Pesach. Even though this is a time bound positive mitzvah, Chazal write that just like women are obligated to avoid Chametz on Pesach so too they're obligated in the mitzvah of eating matzah (as the pasuk juxtaposes eating matza and avoiding chametz). Similarly, they are obligated in all the mitzvot of the night such as the 4 cups of wine, Matzah, Maror, and saying the Haggadah. 
Women are obligated in Chanukah candles since they too were part of the miracle of Chanuka. Thus a man who is away traveling he should have his wife light at home for him to fulfill his obligation. Even if he will come that night later than Tzet HaKochavim (the night to light Chanukah candles), he should still have his wife light. Ashkenazim who have the Minhag that everyone in the household lights and they are able to light where they are should light without a bracha.  See Lighting Chanukah Candles.
The halacha is the women are exempt from Sefirat Haomer (Magen Avraham 489:1). The Shitat HaKadmonim (last page of bava kama, quoted here), however, records the responsa of the son of the Maharam Chavallah in the name of his father who quoted his Rabbi, the Ramban, to say that the women were obligated to count the Sefirat HaOmer (See Ramban Kiddushin 34a). The Maharam Challavah explains that since the time doesn’t cause the mitzvah it’s not considered “Zman Grama”. It happens to be time-bound since of another factor which is that the mitzvah of Sefirah depends on the Korban Omer which itself is bound by time. The Sh”t Maharam Challavah compares it to the obligation on women to eat Shabbat meals which require Birkat HaMazon. That doesn’t make Birkat HaMazon a mitzvah Aseh SheZman Grama because the Birkat HaMazon is obligated as a result of the meal which itself is time bound.
Af Hen Hayu BeOtto HaNes
There's certain which woman shouldn't have been obligated in for one reason or another, but because woman were particularly involved with the story which is being celebrated, woman are obligated. Below are the applications of this principle:
Women are obligated to drink the four cups of wine at the Pesach Seder.
Women are obligated to light Chanukah candles. 
Women are exempt from performing a Brit Milah on a son. The gemara derives this exemption from the pasuk "צוה אותו" and it does not say "אותה". However, many rishonim are puzzled as to why the gemara doesn't simply say that women are exempt since it is a time-bound mitzvah.
Pidyon HaBen is a non-time bound mitzvah. Nonetheless, women are exempt because of an exclusion of the pasuk.
Some say that women have a mitzvah to get married.
Mitzvot that don’t apply nowadays
Turei Even (Chagigah 15) writes that Semicha on a Korban isn’t a Mitzvah Aseh SheHaZman Grama since the mitzvah doesn’t have a fixed time. Regarding Tefillin there’s one day to do it and afterwards the mitzvah is lost and there’s a new Mitzvah to wear Tefillin. However, by Semicha that same Mitzvah could be done any day during the daytime. [See Minchat Elazar 2:47’s second reason regarding the building of the Bet HaMikdash.]
The Rambam (Bet HaBechirah 1:12) writes that everyone is obligated in building the Bet HaMikdash. The questioner in Sh”t Shoel UMeshiv Tanina 3:89 (beginning paragraph s.v. Heneh) inquires as to why women are obligated since it’s a mitzvah that only applies during the day and being a time-bound mitzvah, women should be exempt.
However, the Sh”t Shoel UMeshiv answers that because men are obligated, women are also obligated. The reason for this is since the whole reason of a women being exempt is that women are subservient to their husbands and don’t have time to fulfill time-bound מצות, however since their husbands are obligated, they too can fulfill this mitzvah properly.
Alternatively, the Sh”t Minchat Elazar 2:47 writes that since the mitzvah includes donations to the Bet HaMikdash which can be given at night as well, then it’s not considered a time bound mitzvah.
The Minchat Elazar’s second reason is that since the mitzvah is incomplete and could continued to be fulfilled each day, then, even if the mitzvah doesn’t apply during the night, still it’s considered not time-bound unlike Tefillin which is time bound and once the day passes there’s a new mitzvah to fulfill. [See Turei Even regarding Semicha.]
↑The gemara Kiddushin 29b learns from the pasuk that says "ולמדתם אותם את בניכם" (Devarim 11:19) that the obligation of Talmud Torah applies to men and not women. Next the gemara Kiddushin 34a derives this halacha from the juxtaposition in the pesukim (Devarim 6:7-8 and 11:18-9) between Tefillin and Talmud Torah, just like women are exempt from Talmud Torah so too they are exempt from Tefillin. Then, gemara kiddushin 35a writes that the pasuk in Shemot 13:9 compares Tefillin to all mitzvot to teach us that just like Tefillin is a positive time bound mitzvah and women are exempt so too all positive time bound mitzvot women are exempt. See the gemara there for the full discussion. The Mishna Kiddushin 29a rules that women are exempt from positive mitzvot that are time bound. This is codified by the Rambam (Avoda Zara 12:3), Tur and Shulchan Aruch 17:2.
↑ Rambam Tzitzit 3:9 and Sukkah 6:13 writes that since women are exempt from the Mitzvah of Tzitzit they can't make a Bracha on it. However, the Raavad Tzitzit 3:9 and Tosfot (Eruvin 96a and Kedushin 31a s.v. lo mifkadana) quoting Rabbenu Tam argue that even if you are exempt from a mitzvah you can make a bracha if one wants to do the mitzvah. The Maggid Mishna Sukkah 6:13 explains the Rambam as saying that it is impossible to say VeTzivanu if a person is exempt from the mitzvah.
↑ Rav Elyashiv in Yashiv Moshe (pg 19), Birkat Eitan (pg 61), Rav Hershel Shachter in a shiur on yutorah.org called “Women at Prayer”, Rav Ovadyah Yosef in Halichot Olam (vol 1 pg 59) and Yalkut Yosef (Otzer Dinim LeIsha pg 75), and Hilchot Bat Yisrael (end of chapter 14) write that a woman is obligated since it’s a obligation that applies the whole day and is renewed every day similar to the Shagat Aryeh regarding Zecher Yetziat Mitzrayim in Shema. However, Halichot Bayita 13:1 in name of Rav Shlomo Zalman, Sh”t Teshuvot VeHanhagot 2:129, Sh”t Shevet HaKehati 3:63, Birkat Eitan (pg 62), Vezot HaBracha (pg 185, chapter 20), Sh”t Atret Paz 1:1, Shevet HaLevi 5:23, and Sh”t Rivevot Efraim 3:47, 5:114 write that a women is exempt and some base it on the Magen Avraham regarding Zecher Yetziat Mitzrayim in Shema who disagrees with the Shagat Aryeh.
↑ S”A 565:5 says that women are obligated in Chanukah candles based on Shabbat 23a, Rambam (Chanukah 4:9), and Tur 565. Piskei Maharam Riketani (154) holds women can fulfill a man’s obligation on his behalf. This is also the opinion of Rabbenu Yerucham 9:1, Rokeach Chanukah 226:3, Ritva and Meiri (Shabbat 23a, Megilah 4a), Maharil (Chanukah pg 407). Levush (675), Bach (675), Taz (675:4), Magen Avraham 675:4, Olot Shabbat 675:1, Pri Chadash 675:4, Eliyah Raba 675:6, Sh”t Shar Efraim 42, Shulchan Gavoha 675:6, Mor Ukesia 675:6, machzik Bracha 675:4, Mishna Brurah 675:9. Sh”t Yechave Daat 3:51 writes that since some rishonim and achronim hold one can only light at Tzet HaKochavim one should let his wife light at the right time and fulfill his obligation according to all opinions. The Yechave Daat holds like the Chaye Adam 154:33. Kaf Hachiam 676:25. Chaye Adam adds that Ashkenazim can light without a bracha. Interesting point: S”A 689:2 says a women can read the megillah to fulfill for a man his obligation of megillah, and some hold otherwise. [Bahag (quoted by Tosfot Megilah 4a, Erchin 3a) and Morchedai 4a in name of Ravyah (Megilah 569, 843) hold women can’t fulfill the obligation of a man, but Rashi Erchin 3a, Or Zaruh 2:324, Rambam(Megilah 1), Rif (quoted by Sefer Eshkol 2:30) hold a women can fulfill obligation of a man]. However Smag (brought by Magen Avraham 589:5), Itur (Megilah 113d), Eshkol 2 pg 30 differentiate between Megilah which is like Torah reading but by Chanukah women can fulfill the man’s obligation according to everyone. Also Torat Moadim Chanukah pg 40 says the Behag only held a women can fulfill megilah for a man since a women’s obligation is derebanan and a man’s is from divrei kabalah (Ketuvim). Similarly, Sh”t Maharash Halevi O”C 24 says Chanukah isn’t an obligation on each person but on the household and so a women can fulfill it for a man. Thus even those who say by Megilah a woman can’t fulfill a man’s obligation agree by Chanuka.
↑See Gemara Megillah 4a, Shabbat 23a, and Pesachim 108a-b
↑In Gemara Megillah 4a, Rabbi Yehoshua Ben Levi says that women are obligated in reading the Megillah because they were included in the miracle of Purim. Rashi (Megillah 4a s.v. Af) explains that the decree of Haman applied to men and women equally. Tosfot (s.v. Af) quotes the Rashbam who explains that the gemara means that women are obligated because Ester was instrumental in the miracle of Purim. The Rambam (Megillah 1:1) writes that both men and women are obligated in reading the megillah. Tur and Shulchan Aruch 689:1 codify this as halacha.
↑Gemara Kiddushin 29a, Rambam (Sefer HaMitzvot n. 215)
↑Why does the gemara need to learn from a pasuk that women are exempt isn't it a time-bound mitzvah? Tosfot Kiddushin 29a s.v. otto answers that this gemara is following the opinion who says that there’s no end bound for milah because it can be done after the 8th day even at nighttime. Tosfot megillah 20a s.v. dichtiv answers that milah has karet and so we don’t say that women are exempt from mitzvot aseh with karet. Ramban and Ritva Kiddushin 29a answer that since the mitzvah of milah doesn’t apply to her body, she could have been chayav. Similarly, Tosfot Rid answers that we could have thought that her mitzvah is to be responsible for milah occurring and preparing and that preparation isn’t time-bound.
↑The Ran (Kiddushin 16b) assumes that getting married is just a preparation for the mitzvah of having children. He states that even though women aren't obligated in having children she still has a mitzvah when she enables her husband to fulfill that mitzvah of having children. Therefore, he concludes that there is a mitzvah for women to get married.