This is a common question and research shows that the answer is not commonly known. Here is what I believe to be a comprehensive list of apostles taken, with scripture references from the New Testament.
Jesus is our first Apostle. We read this in Hebrews chapter 3. Jesus then called twelve men to follow him, and these became apostles. It is these that we call the apostles of the Lamb. After Judas fell, he was replaced by Matthias, our 14th person named apostle.
After this there were other apostles, which we call ascension apostles because they were called after the ascension of Christ. The other apostles were Paul, Barnabas and James (the Lord's brother) and some Greek (non Jewish) apostles Apollos, Epaphroditus, Andonicus, Junias, Silas and Timothy. There were also 2 other unnamed apostles. This brings the total to 25 confirmed apostles in Scripture.
After these 25, there are other possible apostles in Scripture. We consider here the Mark, Luke, Jude, Titus and the writer of the book of Hebrews. Four of these authored scripture and this was the foundation of the selection of the canon of the New Testament. The fifth (Titus) was similar in role and position to Timothy who was an apostle.
In addition, in 1 Corinthians 15:7 it mentions "all the apostles" allowing room for other unnamed apostles. There are 5 other named possibles that we are aware of, plus other unnamed possibles.
In some versions of the Bible the word “messenger” or similar is used in english rather than apostle. However in the Greek the word apostolos appears with these references. A literal reading in English does not always convey apostle, but a reading in Greek does.
A complete list:
- Jesus Christ (Hebrews 3:1)
- Simon Peter (Matt. 10:2)
- Andrew (Matt. 10:2)
- James the son of Zebedee (Matt. 10:2)
- John (Matt. 10:2)
- Philip (Matt. 10:3)
- Bartholomew (Matt. 10:3)
- Thomas (Matt. 10:3)
- Matthew (Matt. 10:3)
- James the son of Alphaeus (Matt. 10:3)
- Thaddaeus (Matt. 10:3), or Judas the son of James (Luke 6:16)
- Simon the Zealot (Matt. 10:4)
- Judas Iscariot (Matt. 10:4)
- Matthias (Acts 1:26)
- Paul (Gal. 1:1)
- Barnabas (1 Cor. 9:5-6, Acts 14:4, 14)
- Andronicas (Rom. 16:7)
- Junias (Rom. 16:7)
- James, the Lord's brother (Gal. 1:19)
- Silas (Silvanus) (1 Thess. 1:1, 2:6)
- Timothy (1 Thess. 1:1, 2:6)
- Epaphroditus (Philippians 2:25) - The word apostolos does not appear in most English translations but does appear in the Greek, Strong's word 652, Apostolos.
- Apollos (1 Corinthians 4:6-9 & 1 Corinthians 3:22)
- First of 2 Unnamed Apostles (2 Corinthians 8:23) - in many English versions it says messenger, but in Greek, Apostolos.
- Second of 2 Unnamed Apostles.
Possible Other Apostles
- Jude the Brother of Jesus is considered a possibility. He was considered an apostle by early believers and church patriarchs. (http://en.wikipedia.org/wiki/Epistle_of_Jude)
- Mark - Author of Scripture.
- Luke. Some early Church Fathers considered them to be apostles as they had authored Scripture.
- The writer of Hebrews may have been an apostle as he authored scripture.
- Titus. Similar in position and role to Timothy who was an apostle.
- Possible other unnamed apostles (1 Corinthians 15:7)
Starting with the 25 confirmed apostles in Scripture, plus the 5 named possible apostles you have a total of 30, not withstanding the Scripture referring to "all the apostles."