Much of the confusion is the result of confusion over the meaning of the word eperotema. The NIV translates this word as "pledge." The KJV and NKJV translate this word as "answer." The word eperotema took on the meaning of "pledge" or "answer" in the second century in legal documents such as the Justinian code but there is no evidence that it had this meaning at the time of the writing of the New Testament. As Totten points out the most common translation error is to see the parallel between "flesh" and "good conscience." Eperotema comes from the verb eperotao which means "to ask" or "request." So it is rightly translated by the RSV and NASB as "appeal." Baptism is an appeal or request to God for a good conscience. The translation of "pledge" seems to be driven more by theological presuppositions than by solid lexical evidence and context. Baptism now saves you because it is an appeal to God for a good conscience and God grants that request. Peter is not saying that baptism now saves you because baptism is a promise you made to God that you have a good conscience.
Translations that substitute "answer/pledge" for "request/appeal" also tend to confuse the Greek grammar just to make sense of it all. They make the good conscience the source or agent of the pledge. But this completely misses the parallel between "flesh" and "good conscience" found in the Greek. If the good conscience is the source or agent of the pledge then it would seem that "flesh" would have to be the source or agent of the removal of dirt which wouldn't make any sense at all and which no translation to my knowledge does.
Baptism is not the removal of dirt from the flesh.
Baptism is an appeal to God for a good conscience.
1 Peter 3:21 comes immediately after a passage which speaks of how God saved Noah through the water. This seems unusual in some ways. Ordinarily we would think of God saving Noah through the ark and some commentators have tried to go this route but the passage is pretty clear. God saved Noah through the water. God saved him from the unbelieving world. God destroyed the unbelieving world through the waters of the flood but saved and Noah and his family by using the water to lift him into safety while in the ark. Peter literally says that baptism is the antitype of the flood which would make the flood the prototype. Baptism is the greater fulfillment of what happened in the flood.
I came across the following rather unfortunate poor translation in the EOB:
This is an antitype of baptism, which now saves you. Baptism is not the putting away of the impurity of the flesh but the appeal of a good conscience {in your relationship} toward God through the resurrection of Jesus Christ.As a whole I really like the EOB. It's translated by Eastern Orthodox Christians and based on the New Testament text used in the liturgy. Unfortunately, most modern translations are based on a text created in the academy and then translated by Bible societies. Other sections of the EOB are actually translated very well especially those passages dealing with the sacraments. But this one is not. It confuses the antitype with the prototype and says that the flood is the antitype of baptism. It also says that baptism is "the appeal of a good conscience toward God." I've unsuccessfully tried to contact those responsible for the translation and I'm sure they would be willing to correct it if I could find the right person to tell. They also depart from their own Greek text by having "saves you" instead of "saves us."
The ESV, RSV, and NASB already do a fine job but this is my own proposed translation:
The antitype baptism now also saves us, it does not remove dirt from the body but asks God for a clear conscience, through the resurrection of Jesus Christ.