That phrase is so often quoted out of context and contrary to Luther’s intention, that I thought I’d post the entire context of the phrase. It’s from a letter he wrote to Melanchthon in 1521.
If you are a preacher of grace, then preach a true and not a fictitious grace; if grace is true, you must bear a true and not a fictitious sin. God does not save people who are only fictitious sinners. Be a sinner and sin boldly, but believe and rejoice in Christ even more boldly, for he is victorious over sin, death, and the world. As long as we are here we have to sin. This life is not the dwelling place of righteousness but, as Peter says, we look for new heavens and a new earth in which righteousness dwells. It is enough that by the riches of God’s glory we have come to know the Lamb that takes away the sin of the world. No sin will separate us from the Lamb, even though we commit fornication and murder a thousand times a day [that’s not a recommendation! T.W.] Do you think that the purchase price that was paid for the redemption of our sins by so great a Lamb is too small? Pray boldly–you too are a mighty sinner. (Luther’s Works, 48:281-282)
UPDATE: Here is another translation of the above passage (thanks to Caspar Heydenreich of Beggars All).
Balaam's Ass 
You are right in your criticism of the abuse of this phrase. However, that’s not the whole context in your quote. Here’s an address for the full letter in a more literal translation from a fellow church member of mine, Erika Flores, which she performed for Project Wittenberg:
http://www.iclnet.org/pub/resources/text/wittenberg/luther/letsinsbe.txt
Note that the phrase “sin boldly” is not even a correct translation. Here is the more literal understanding: “Be a sinner, and let your sins be strong, but let your trust in Christ be stronger, and rejoice in Christ who is the victor over sin, death, and the world.”
Thanks for that link, and the clarification.
Tim
I used that translation on the “Purpose Driven Drinking” blog. It goes to that same page Caspar the Friendly Ghost provided but I put a picture of “License to Sin Boldy” from Old Lutheran.
I was doing more research on this and discovered that this letter of Luther’s was originally in Latin. The German text translated by Erika Flores was Johann Georg Walch’s German translation of the original Latin. Walch translated many of Luther’s Latin writings into German for the “St. Louis Edition.”
“Let your sins be strong” probably gets more to Luther’s intended meaning, based on the context, but Luther did actually write, “pecca fortiter”. So, it turns out “sin boldly” is an unfortunately accurate translation of the actual words Luther penned.
Here is the original Latin version of Luther’s letter to Melanchthon in the Weimar Edition. The words in question are near the bottom of page 372:
http://archive.org/stream/supplwerkebriefwecr0302luthuoft#page/370/mode/1up
Thanks. That’s great.
“Pecca fortiter” can also mean “sin strongly”, which seems to fit better since the sentence continues, “sed fortius fide et gaude in christo” (but more strongly have faith and rejoice in Christ). This also fits better with the plausible explanation that Luther is simply paraphrasing his understanding of Romans 5:20-21, “Woaber die Sünde mächtig geworden ist, da ist doch die Gnade viel mächtiger geworden” (But where sin becomes strong, nevertheless grace becomes even more strong).