Taraaweeh... 11 or 20 Rakats?

Assalam-o-Alikum

Ramadan Kareem...

It is a very controversial issue nowadays that Taraweeh should be 11 (8+3) Rakats or 20 rakats

Both the ways are correct and proven by Sunnah. It is the choice of the imam... There is no number set by the Prophet PBUH Regarding the Rakats... however the Prophet Mohammad PBUH said that it should be of 2 rakats... 

The witr can be of 1 Rakat, 3, 5, 7  and 9 rakats 

Evidence of 11 (8+3) Rakats is the hadith of Abu Salamah ibn 'Abd al-Rahmaan, who asked 'Aa'ishah (may Allaah be pleased with her), "How did the Messenger of Allaah (peace and blessings of Allaah be upon him) pray during Ramadaan?" She said:
"He did not pray more than eleven rak'ahs in Ramadaan or at other times. He would pray four, and do not ask how beautiful and long they were, then he would pray four, and do not ask how beautiful and long they were, then he would pray three. I said, 'O Messenger of Allaah, will you sleep before you pray Witr?' He said, 'O 'Aa'ishah, my eyes sleep but my heart does not.'" 

Narrated by al-Bukhaari, 1909; Muslim, 738 

Evidence of 20 Rakats is the favoured view of 3 Imams... that is of Imam Ahmed, Imam Abu Hanifa, and Imam Al-Shaafai...

Also... Imam Malik was of view that it 36 Rakats...

Shaykh al-Islam Ibn Taymiyah said:

 If a person prays Taraaweeh according to the madhhabs of Abu Haneefah, al-Shaafa'i and Ahmad, with twenty rak'ahs, or according to the madhhab of Maalik, with thirty-six rak'ahs, or with thirteen or eleven rak'ahs, he has done well, as Imam Ahmad said, because there is nothing to specify the number. So the greater or lesser number of rak'ahs depends on how long or short the qiyaam (standing in the prayer) is.  

For further Clarification... I have attached a book, Title Concerning Taraweeh, Fatwa by Sheikh bin Baaz...

Also you may consider reading the following links...

http://www.islamqa.com/en/ref/9036/

http://www.islamqa.com/en/ref/38021

And Surely Allah Knows the best...