Dr. Peter Masters has written an interesting article in the Sword and Trowel on the cessation of the sign gifts, and addresses some of the popular arguments used against Cessationism in the process. While not necessarily agreeing with everything, I do think most of the arguments are valid. An excerpt:
Does the Bible teach definitively that the charismatic gifts have ceased? Can cessationism (the view that they have ended) be proved? Some say that the cessation of the gifts cannot be conclusively proved from Scripture.
We believe, however, that the ceasing of revelatory and sign-gifts in the time of the apostles is very plainly taught in God’s Word, so plainly, in fact, that the opposite view has only seriously appeared in the last 100 years or so.
The term cessationism comes from the great 17th-century confessions of faith, such as the Westminster and Baptist confessions. These both use the same word. Speaking about how God has revealed his will and committed it to the Scriptures, the confessions say, ‘Former ways of God’s revealing his will unto his people being now ceased’. This word does not actually come from the Bible, but the doctrine does.
Not only has revelation been completed and ceased, but so have the signs that revelation is in progress. Here is a brief summary of six biblical proofs that the revelatory gifts have ceased (visions, words of knowledge, words of wisdom, and prophecies), and also the sign-gifts (healings and speaking in tongues). God still heals, of course, but in answer to prayer, and not through the hands of a gifted healer.