Man I wish I could remember I was hearing a sermon on this just the other day! But i'll give it my best shot.
Rom 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
Rom 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
Rom 6:5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
Rom 6:6 Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
Rom 6:7 For he that is dead is freed from sin.
Rom 6:8 Now if we be dead with Christ, we believe that we shall also live with him:
Rom 6:9 Knowing that Christ being raised from the dead dieth no more; death hath no more dominion over him.
Christ took our place on the cross, endured the wrath of God, and resurrected. The resurrection was a proof that he really did take our own sins, and as a result saved us. He took our old man on the cross and killed him there, by his resurrection we live. The whole idea being that since we died with Christ on the cross, he rose in newness of life, giving us eternal life because the law, the curse, etc. etc. was killed on that cross on our behalf. The only problem being that the old man likes to come down from the cross and harass us. Which is why he wrote Romans 7.
Another similar thought is this...
Rom 8:3 For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
Rom 8:4 That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
My thoughts sound pretty scattered, in my mind it's pretty solid but i'm not having a very good time presenting it as best as possible.