Gemara

(Beraisa #1): The Tamid is offered before the Pesach; the Pesach precedes the Ketores; and the Ketores precedes [lighting] the Menorah;

(Beraisa #2): The Tamid is offered before the Ketores. The Ketores precedes the Menorah. The Menorah precedes the Pesach;

(Beraisa): The Ketores is the only thing offered before the morning Tamid;

It says "v'Hiktir Alav Aharon Ketores Samim ba'Boker ba'Boker." Therefore, it is before the Tamid, about which it says 'Boker' only once.

Kerisus 6a (Beraisa): If any spice was lacking, he is Chayav Misah.

Yoma 33a: Abaye gave the order of what is burned on the Mizbe'ach, according to Aba Sha'ul... they do Zerikah (throw the blood) of the Tamid, then fix two Neros of the Menorah, then offer the Ketores, then the limbs of the morning Tamid...

38a (Beraisa): Beis Avtinas did not want to teach others how to make the Ketores. Chachamim sent for professionals from Alexandria. They knew how to compose the Ketores like them, but they could not get it to rise straight.

Rishonim

Rashi (59a DH Tehei): Nothing is burned [on the Mizbe'ach] before the morning Tamid other than the Ketores.

Rashi (38a DH Leha'alos): The professionals from Alexandria did not know the herb that makes the smoke rise straight.

Poskim

Rema (OC 132:2): One should say Pitum ha'Ketores evening and morning after Tefilah.

Taz (2): In Pesachim, we say Ketores is the only thing offered before the morning Tamid. Shacharis was enacted corresponding to the morning Tamid (Berachos 26b). If so, we should say the Ketores before Shemoneh Esre! Why do we delay it until after Tefilah? I answer that Ketores is burned on the Mizbe'ach before the Tamid, like Rashi says, but Shechitah and Zerikah of the Tamid preceded the Ketores, like Abaye taught. If so, Shemoneh Esre is in place of the blood of the Tamid. Therefore, the Ketores is after it. Another difficulty is that Abaye mentioned Ketores much later.

Note: The Mishbetzos Zahav did not understand this. Only fixing two Neros of the Menorah separates between the blood of the Tamid and the Ketores! Mekor Chayim (cited in Shulchan Aruch ha'Shalem, Hagahah 19) switches the order of the words of the Taz, and puts this question from Abaye before the Taz' first answer. (This helps, but it does not answer why he said 'much'. Perhaps he means that it was much after Shechitah, but Abaye did not mention Shechitah.)

Taz (2): It seems to me that Shemoneh Esre is in place of offering the limbs of the Tamid. Parshas ha'Tamid is in place of Shechitah and Zerikah. We do not need something else in place of them! Rather, it is in place of the limbs. The Tur (235) says that Ma'ariv is in place of limbs that were not consumed during the day. This shows that Minchah is in place of limbs burned during the day. Therefore, I say the Ketores before Baruch she'Amar, so it will be between [what corresponds to] the blood of the Tamid and the limbs. Even though the Tur wrote that it is after Tefilah, it seems that also this is correct.

Magen Avraham (3): The Ari Zal says not to say it at night. Perhaps he (the Rema) means that one says it after Minchah or before. It is not clear why we say it after Musaf [on Shabbos and Yom Tov]. All agree that Ketores is before Musaf! It pertains to the Tamid. Perhaps we say it then to finish amidst Divrei Torah. Kesavim [of the Ari Zal] say that it is to chase away Klipos (shells of Tum'ah). The Shlah says to say it at Shacharis, before and after Tefilah.

Mishnah Berurah (13): "Evening" refers to after Minchah or before. They did not burn Ketores at night.

Kaf ha'Chayim (18): Whoever says Parshas Ketores every day is saved from all bad matters, mishaps, evil thoughts and harsh judgments. He will not be harmed, the entire day, and the Satan cannot rule over him. He must have Kavanah in it (Zohar). One should have intent in saying it, not for his benefit, rather to be pleasing to Hash-m. From its attributes, we know how pleasing it is to Hash-m. When saying it, one should look at the letters. If one says it quickly, by heart, there is no benefit from it.

Kaf ha'Chayim (19): It is proper to say it after Parshas ha'Tamid, and after Tefilah after Kaveh, and at Minchah between Parshas ha'Tamid and Ashrei, but not afterwards, like the Shlah says. This is the custom of Eretz Yisrael, Mitzrayim, Turkey, and cities of Ivropa (Europe? - PF). Where this is not the custom, one should do so covertly.

Rema (ibid.): We say first Ein Keilokeinu.

Noda bi'Yehudah (1 OC 10): We say Ein Keilokeinu first because Pitum ha'Ketores brings wealth. One should not say that he became wealthy due to his valor, therefore we acknowledge that everything is from Hash-m and it is proper to bless Him.

Rema (ibid.): Some write to read Pitum ha'Ketores from a written text, and not say it by heart, lest one skip one of the ingredients, and we say that if one omits an ingredient, he is Chayav Misah.

Beis Yosef (133 DH v'Alecha): The other matters [after the 11 spices listed] are only to fix, e.g. to make the Tziporen pungent, or make the smoke go up straight. Therefore, the Torah did not count them among the ingredients. (We expound that there are 11 ingredients.) It seems that one is not liable if he omitted them. We would have used Mei Raglayim (urine, or a foul smelling liquid) in place of Kafrisin wine, if not that it is dishonorable! Perhaps there is not even an Isur for omitting the other matters. They are just for the ideal Mitzvah. We say in Yoma (38a) that others knew how to compose the Ketores, just they could not get it to rise straight. It seems that they lacked Ma'aleh Ashan. They tried offering it inside the Heichal, for one may not burn Ketores [like the composition of that in the Mikdash] outside the Mikdash. The same applies to other matters that are merely to fix the Ketores.

Rebuttal (Be'er Sheva Kerisus 6a DH Chisar, brought in Magen Avraham 5): Yoma 53a says that even if he is exempt for entering, e.g. he was Shogeg about entering and Mezid for burning (Pasul Ketores), he is liable for burning. Even if he omitted only Ma'aleh Ashan, he is Chayav Misah. If so, one must be careful with the 11 ingredients and Ma'aleh Ashan. We are not so concerned about the other ingredients [not listed among the 11].

Beis Yosef (DH Kasav): Mahari Avuhav says that one should read Pitum ha'Ketores only from a written text, lest he omit an ingredient, and be Chayav Misah for an incomplete recitation, just like for burning incomplete Ketores. Perhaps this is why some places do not say it, even though they say [the other] Korbanos. I would have said that the Kohen will be Chayav Misah when he enters the Kodesh ha'Kodoshim on Yom Kipur [without valid Ketores], like Rashi explains. Even if you will say that one is liable for offering it [incomplete] any day in the Heichal, there is no source to obligate Misah for reciting. Also, one is liable only for omitting one of the 11 ingredients. It is easy to be careful about them. This is not a reason to refrain from saying it.

Magen Avraham (5): Misah is only for burning, but not for reciting. Also, it is only if one was Mezid. Therefore, meticulous people say it every day.

Chachmas Shlomo: Reciting it is not truly like offering it. If it were, we would not be allowed to recite it, for we are Tamei Mes and Zarim! Perhaps this is the Magen Avraham's reason why there is no Misah for reciting.

Rema (ibid.): Therefore, the custom is not to say it during the week, for people rush to go to work, and we are concerned lest one skip an ingredient.

Mishnah Berurah (17): Some say that those who say it only on Shabbos, since it is not so fluent in their mouths, should say it from a Sidur.