Umar ibn al-Khattab changed during his rule many things in Islam.
1. Athaan: He removed (Hayya Al Khairul 'Amal) from the Athaan of the Prophet (SAWA) and added in the Athaan of morning prayer (Assalatu Khairun Minannawm) which was never in the Athaan of the Prophet. (Al-Muwatta'; 42 and Mussannaf ibn Abi Shaibah; 1/189, Sunan Al-Tirmithi 1/381)
2. Salah: He ordered his people to fold hands during prayers which was never done by the Prophet (SAWA). Shaikh Sayyed Saabiq from Al-Azhar admitted in his book ( Fiqh al-Sunnah) that there no single authentic Hadeeth that the Prophet ever folded his hands during prayers.
3. Fadak: He denied the rights of Fatimah (AS) in Fadak which was gifted to her by the Prophet (SAWA) during his life.
4. Taraweeh: He started a congregational prayer (Taraweeh) which was never done during the time of the Prophet (SAWA). Umar himself admitted that it is Bid'ah ( Saheeh al-Bukhari and Saheeh Muslim). He called it a good Bid'ah.
5. Mut'ah: He banned an Islamic marriage called Mut'ah which was allowed in Quran (4:24) and was practiced during the time of the Prophet and even during the government of Abu Bakr. Umar said: I am banning the Mut'ah which was allowed during the time of the Prophet. (Musnad Ahmad bin Manbal; V.3, P. 304).
These are just few examples and you can find more in the very valuable book (Al-Nass Wal Ejtuhad) by Sayyed Sharafuddin al-Musawi and Peshawar Nights which are available online on many sites e.g. www.aqaed.com. And www.al-Islam.org