There are 8 Non-Pauline Letters of the New Testament: 

Books/When:
1. Hebrews (60s AD)
2. James (49 AD)
3. 1st Peter (64-65 AD)
4. 2nd Peter (64-68 AD)
5. 1st John (85-95 AD)
6. 2nd John (85-95 AD)
7. 3rd John (85-95 AD)
8. Jude (60s AD)

Who:
The Letter to the Hebrews was originally attributed to Paul; however the true author of the Letter to the Hebrews is anonymous.

According to tradition, the Letter of James was attributed to the brother of Jesus, James the Just.

The Letters of Peter and John have been traditionally attributed to the apostles of the same name.

The Letter of Jude, which is the shortest book of the New Testament, is often attributed to Jesus' brother Judas (*not to be confused with Judas Iscariot, Jesus' betrayer).