I do not think you can have discussion about cessationism without mentioning 1 Corinthians 13:
1 Corinthians 13:8-10
8 Love never fails. But where there are prophecies, they will cease; where there are tongues, they will be stilled; where there is knowledge, it will pass away. 9 For we know in part and we prophesy in part, 10 but when completeness comes, what is in part disappears.
The question is, what Paul talking about? It seems that at some point in time, either in the past or in the future these gifts will not be taking place or would have stopped taking place. When will this happen? Paul gives the answer in verse 10, "...when completeness comes".
So the cessationist argument, using this as proof text, generally is centered around the meaning of 'completeness'. They would argue the completeness came at the end of the apostolic age.
Mark Driscoll gives a very thorough treatment of the text here, in which he comes to an anti-cessationist conclusion, but extremely thorough none-the-less, and worth a read.