Paul tells us to do both, depending on the context (emphasis mine below).
Eph. 2:11-13. Wherefore remember, that ye being in time past Gentiles in the flesh, who are called Uncircumcision by that which is called Circumcision in the flesh made by hands; That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers to the covenants of promise, having no hope, and without God in this world: But now in Christ Jesus ye who sometime were far off are made nigh by the blood of Christ.
Phil. 3:13-14. Brethren, I count not myself to have apprehended: but this one thing I do, forgetting those things which are behind, and reaching forth unto those things which are before, I press toward the mark for the high calling of God in Christ Jesus. [I think that the direct reference is to Phil. 3:7, "But what things were gain to me, those I counted loss for Christ."]
So, in one sense we should forget our past life, and in another we should remember it. A good example is Joseph in Gen. 41:51, "And Joseph called the name of the firstborn Manasseh: For God, said he, hath made me forget all my toil, and all my father's house." Obviously he had't forgot these things entirely, else he wouldn't have mentioned them. The point was that he wasn't letting them hinder him in the present, with God's help. The same is true of Paul: he hadn't totally forgot his past (Phil. 3:4-6), but he was pressing forward in his knowledge of Christ and not clinging to his previous righteousness. In Eph. 2:11-12 we're emphatically told to remember some things from the past, which are actually negative, to accentuate something positive in the present (v. 13). So there is a place for remembeing the past, as long as it edifies and doesn't hinder us in the present.