Has there been a anime that used its OP as ED and/or vice versa? Running along the list of unanswered questions, I came along the question about different EDs each episode. And I wondered, has there been an anime that actually switched its OP and ED during the runtime of the show? And if so, which one(s) would that be?
This is not uncommon - a number of shows will have a first episode with no song at the beginning, and with the OP at the end of the episode. I'll pull in some examples of this later. 

There are also somewhat more unusual cases like Madoka (as Memor-X points out in the comments), in which "Connect" (usually the opening) was used as the ending song in episode 10.



But, for a particularly amusing example of this, look at Hanamonogatari. In the Monogatari series, OPs are always sung by the voice actors, and EDs are sung by other singers. Hanamonogatari's OP was "the last day of my adolescence" (by Kanbaru Suruga / Sawashiro Miyuki), and the ED was "Hanaato -shirushi-" (by Kawano Marina). 

Since Hanamonogatari was broadcast as a continuous ~2-hour long special, the OP and ED each only ran once - but the ED was played at the beginning, and the OP was played at the end! Imagine that!

(I think this is because the OP visuals and lyrics are spoilery for Hanamonogatari, whereas the ED visuals/lyrics aren't? But I'm not sure about that.)