When do we say “Alenu L'shabe'ach”?

Question

What are all the times when we say the t'fila beginning with the words "עלינו לשבח" commonly known as "Alenu"?

Answer 1

Here are some!

For Nusach Ashkenaz:

• At the end of shacharis (when there's no mussaf)
• At the end of mincha
• At the end of ma'ariv
• At the end of mussaf
• At the end of kidush l'vana
• At a b'ris
• Shemoneh Esrei of mussaf on Rosh Hashanah
• Shemoneh Esrei of mussaf on Yom Kippur

For Nusach Chabad:

• All of the above (except, perhaps, after a bris: it's not official Chabad minhag to say Aleinu then, and I haven't seen it done, although I understand that some Chabad communities do so)
• At the end of n'ila
• After birkas hachama

For Sephardim:

• At the end of shacharit (when there's no Mussaf)
• At the end of mincha
• At the end of arvit
• At the end of mussaf (even on Yom Kippur)
• Shemoneh Esrei of Mussaf on Rosh Hashanah
• Shemoneh Esrei of Mussaf on Yom Kippur

Answer 2

In the Shemoneh Esrei of Mussaf on Rosh Hashanah. If I'm not mistaken, that is where the tefillah was originally established (see here).

Answer 3

For sepharadim:

• At the end of shacharit (when there's no Mussaf)
• At the end of mincha
• At the end of arvit
• At the end of mussaf (even on Yom Kippur)
• Shemoneh Esrei of Mussaf on Rosh Hashanah
• Shemoneh Esrei of Mussaf on Yom Kippur

Answer 4

It all depends on when your finish your tefillah.

If one were to daven shacharit at netz and the mussaf at chatzot (which is the theoretical ideall, at least for a yachid and on a day like rosh chodesh where there is no issue of seudah; see the first biur halacha in 286) then he should say aleinu after shacharit and again after mussaf. Similarly, if mincha and maariv are being recited back to back then no aleinu should be said just like how we omit it from most prayers on Yom Kippur.

See Mishna Brura 132 sk 7