Romans 3:28
"Therefore we conclude that a man is justified by faith without the deeds of the law."

"Therefore"
The usage of this word denotes that Paul said what he said previously so that he could say this.  The preceding verse is then part of the immediate context. 

Romans 3:27
"Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith."

There are two laws in view in this context.  So which law justifies and which law does not?  The faith which justifies in verse 27 is the law of faith mentioned in verse 26.  Law is a rule of conduct.  Many people who hold to the doctrine of justification by faith only often use this verse out of context as a proof text in support of their doctrine. 

The law of faith goes by other names in scripture:

The law of faith (Romans 3:27).
The law of the Spirit of life (Romans 8:2).
The perfect law (James 1:25).
The royal law (James 2:8).
The law of liberty (James 2:12).
and the Law of Christ (Galatians 6:2)

All of these terms point to a rule of conduct for the Christian to observe.  The "deeds of the law" is therefore a reference to the Levitical Law and Paul is drawing a contrast between it and the law of faith under which we live now. 

Romans 3:28 Paraphrase:
Therefore we conclude that a man is justified by the law of faith without the ordinances of the Law of Moses.