When will the US stop making 1 dollar bills?

While the US is unlikely to stop printing $1 bills in the near future there's a very slowly increasing realization in Congress that a considerable amount could be saved by doing away with $1 bills in favor of coins.

About 50 other countries have already done so, and claims that their citizens would never accept the new coins proved to be unfounded. However those other countries' coinage policies are determined by their Treasury Departments or Finance Ministries, while coinage changes in US require Congressional approval. That allows politics to muddy the waters significantly, especially because Crane Paper (the single supplier of all paper for $1 bills) lobbies relentlessly to maintain their profit margins.

At some point the inefficiencies of the $1 bill will outweigh the politics of the situation, just like the incredible waste of using English measurements in an otherwise metric world will eventually force the US to convert. That time will not come soon though, unless current attitudes shift more than they have.