Is it hypocritical for Paul to circumcise Timothy in Act 16:3? Acts 16:1-3 (NASB)
   1 Paul came also to Derbe and to Lystra. And a disciple was there, named Timothy, the son of a Jewish woman who was a believer, but his father was a Greek, 2 and he was well spoken of by the brethren who were in Lystra and Iconium. 3 Paul wanted this man to go with him; and he took him and circumcised him because of the Jews who were in those parts, for they all knew that his father was a Greek.


The answer could be right here 'because of the Jews who were in the those parts', however, it seems hypocritical especially given other texts like Galatians 5, where he is harshly admonishing the Galatians who were even thinking about getting circumcised, presumably (and similarly) because of the Jews as well.


  Galatians 5:2 (NIV)
  Mark my words! I, Paul, tell you that if you let yourselves be
  circumcised, Christ will be of no value to you at all.
The answer is perhaps best given in 1 Corinthians 9:20-23 (emphasis added):


  To the Jews I became as a Jew, in order to win Jews. To those under the law I became as one under the law (though not being myself under the law) that I might win those under the law. To those outside the law I became as one outside the law (not being outside the law of God but under the law of Christ) that I might win those outside the law. To the weak I became weak, that I might win the weak. I have become all things to all people, that by all means I might save some. I do it all for the sake of the gospel, that I may share with them in its blessings.


Paul understood, as did Peter (See Acts 10 and Cornelius), that they were no longer bound by the Jewish law. Peter saw that he should no longer call unclean what God considered clean. This specifically included pork and unclean animals.  

So, before God, Timothy did not need to be circumcised. However, if your target audience involves Jews, to whom the "uncircumcised" were deplorable, then it is appropriate to be circumcised for the sake of the hearers. Paul said that he became as Jew to win the Jews.  He became weak to win the weak, etc.

Hudson Taylor followed this example as a missionary in China as he donned the clothing and hair style of the Chinese, thereby identifying with them culturally.

So, again, it is appropriate to not offend those with whom you wish to share the gospel, so that what is unimportant does not become an unnecessary stumbling block to your hearers.