"Trials" for me. It's not a very deep episode but it has all the humor and fun that is or IMHO should always be part of Trek at some point. Yes, I want the moral dilemmas, conflicts etc. but every now and then I also want the fun. And that's where this episode delivers in spades. So much, in fact, that it's very rewatchable IMHO.
I think "Darmok" is ok but in hindsight I find the premise to be a problem. The message that they're tying to transport is somewhat marred by the feeling that it seems silly (to me anyway) that the universal translator happens not to work here or works in a way that causes the alien captain to keep spouting out seemingly random words. They happen to come together as metaphors so that Picard can understand them and finally piece together what the alien is trying to say (which is another contrivance IMHO).
Also, I think the episode isn't all that deep, really. Yes, it's got a nice message but IMHO that's about it. It could be summed up far more easily and to the point and not so dragged out as is the case here.
The more I think about it, the more I think this poll is a bit problematic. As I mentioned, "Trials" represents one part of what I like about Trek as a whole or what I expect from Trek. To really represent all the different aspects, you'd need more than just one episode per show, I think.
So, for example, if I were choosing episodes from DS9, I'd probably name shows such as "Emissary" (the human condition is closely examined), "Duet" (taught person-to-person drama stemming from major historical events), "The Visitor" (an intimate personal drama), "Call to Arms" (or many others from S5 - 7 with sweeping political and military changes), "In the Pale Moonlight" (political and moral drama), and, finally something like "Trials" (as mentioned: fun).
I really think you can't boil it down to just one episode per show.