The best idol turned actor/actress would be Eugene or Yoon Kye-sang. I also really liked Soo-young in Dating Agency: Cyrano and Hello Schoolgirl. She shows a lot of promise as an actress. I would like to see her in more lead drama roles.
I totally agree @Yumiya, Park Yoochun is the best!! But there are other idols who's become great actors/actresses too. Bi Rain totally amazed me with his performance in A Love to Kill for example :)
Yoon Eun Hye,Matsumoto Jun,Lee Jun Ki,Lee Seung Gi,Kim Jae Joong,Park Yoochun and Yamashita Tomohisa are the best ones for me .. They are not only talanted singers,but also good actors (for Eun Hye actress :d) .
Lee Jun Ki is actor who sings....so he doesnt count. No Min Woo, he started like member of TRAX, become famous and after that started acting Jung Yong Hwa, he was and is member of CNBLUE and started acting career kinda lately Kim Hyun Joong, he was member of SS501 before he started acting and he still sings now there is many more ....
Sugar - Hwang Jung Eum & Park Soo Jin
Baby Vox - Yoon Eun Hye & Lee Hee Jin
Chakra - Jung Ryeo Won
SES - Eugene
Fin.K.L. Sung Yu Ri & Lee Jin
Kim myung soo of infinite
Gikwang! Have you seen him in 20s!? Sooo adorable! :)
Kim Hyun Joong. His acting wasn't so great on Playful kiss or BOF but he has developed. In Inspiring Generation, he was kinda great. And I don't really know why but I find him sooo attractive, even those earlier dramas that he has been so robotic. He is still so adorable <3

Siwon and Donghae from Super Junior. I know they've been mentioned in this topic earlier but I think they can act surprisingly good. And since I love Donghae.. There is no wonder why I wouldn't like them :D

IU acts pretty well.  D.O. is fantastic.

I'm currently watching 'Military Prosecutor Doberman' and Kim Woo Seok is crazy good in that one. Someone give him an award for best psycho-acting of the year please.

I love idol actors but Junho outshines them all

 Vitalia:
Yoon Eun Hye,Matsumoto Jun,Lee Jun Ki,Lee Seung Gi,Kim Jae Joong,Park Yoochun and Yamashita Tomohisa are the best ones for me .. They are not only talanted singers,but also good actors (for Eun Hye actress :d) .

I don't think YamaPi is a good actor, not even decent where he shows no emotion.