I recently discovered a TNG fan film, but it's a little more unusual than you might think.
Offically, it's porn parody, but they actual wrote a real story for it, which involves The alternate universe Tasha Yar from Yesterday's Enterprise being found by by Picard's Enterprise, and naturally Sela and the Romulans are involved. Apparently the offical dvd release had a second disc with all the xxx content edited out and it still makes a 45ish minute story. The edited version is on youtube as Star Trek A Tale of Two Cities, and it overall looks pretty good. The production values are pretty similar to the best fan films, but there will be the odd bad wig and iffy prop. The actor who plays Picard is the same actor who plays him in the Intrepid fan films, and it's startling how much he resembles Patrick Stewart. For what it's worth a stunt double is used for his sex scene in the XXX content.
I only watched a little just to get a feel for what I thought of it, as I'm in the middle of a Trek marathon, and am going to wait and watch this in it's entirety when I get thru TNG again (I'm in the middle of TOS season 1 right now, so it'll be awhile).