Here's a fun one from a story told at a panel from a con:

Siddig (Dr Bashir) was asked when he believed his character was replaced by the changelings, and did he make any acting choices related to that. His response was utter confusion and surprise, because he never knew that Dr Bashir had ever been replaced in the storyline. During the time of filming, he hadn't been reading the full scripts, only memorizing his lines, because he was playing too much Ultima Online.