Apothecary, beggar, ill gotten gains, counting house, settlers/bustling village, fountain, Coppersmith, stables, storyteller
When you consider how many cards there are now, that's a puny amount. And half of the ones you mentioned don't even count:
Beggar is only good if there are other cards with Copper synergies on the board. You can't win a game just by gaining Coppers; you actually have to do something with them.
Ill Gotten Gains: Same thing here. It gains Coppers, but that's not the same as actually having synergy with them. You'll still want to trash the Coppers after gaining them if you can. The Coppers are more of a penalty to prevent it from becoming too powerful.
Settlers is extremely unreliable. Usually you only want to use the Copper ability in the beginning before you've trashed them.
Storyteller: You are aware that Storytelling Coppers doesn't actually increase your handsize, right? This is another case where it can deal with the Coppers but it would very much prefer not to.
It's also worth noting that
Counting House and
Coppersmith are absurdly weak and need a large amount of support to be worth it.
Fountain is similar in that it needs support to be worth it.
With
Stables you can often get away with not trashing Coppers but it's still often a good idea to trash at least a few.
Apothecary is the only card that can support a Copper strategy on its own. And even then, it starts dudding pretty fast.
Once again, I have to ask what sorts of games you're playing. Do you really never trash?