In general, qunoot (raising hands to face level and supplicating to Allah while standing in prayer) is only ever in the second rak'ah. This is also the last rak'ah for any prayer that has two raka'at, but it is not the last rak'ah for prayers of 3 or 4 raka'at.
However, there are some special case exceptions, including the Friday prayer, Eid prayer, and Prayer of signs (salaat al-ayaat), among others.
According to the ruling of Grand Ayatullah Sayyid Sistani, one of the most popularly followed Ayatullahs today:
Ruling 1103. In all the obligatory and recommended prayers, it is recommended to perform qunūt before the rukūʿ of the second rakʿah. However, in the shafʿ prayer, one must perform it with the intention of rajāʾ. In the witr prayer – despite it being only one rakʿah – it is recommended to perform qunūt before rukūʿ. In the Friday prayer, each rakʿah has a qunūt. Ṣalāt al-āyāt has five qunūts, and the Eid al-Fiṭr and Eid al-Aḍḥā prayers each have a number of qunūts in the two rakʿahs, details of which will be explained in their own place.
Note that in all cases, qunoot is recommended only, and omitting this act (even intentionally) will not invalidate the prayer.