If it's Cards that, when played twice by a Golem will never give you more benefit than they can give you the first time already one could construct some cases where Library profits from the second play , for example if you set aside some action card, than only draw up to 6 cards and take the action card with the second Library. Of course, if you knew your exact deck before, you could have seen that you will only draw 6 cards and don't set the one aside the first time, but that would mean you have ideal tracking of your deck, so the Library saves you this and this is a small benefit that you get from playing it twice. While only picking up n-2 Coppers the first time and than 2 the second time with the CH is unnessessary.
Also, you could use this trick to force a reshuffle, and pick up an additional card with the second Lib
So if that's the category, I would nominate Secret Chamber .