I've watched all 10 episodes of the fan-made web series "Star Trek Continues." It's very faithful to the feel of the original series and its production values are top notch - making it look very much like the original (all the sets, sound effects and music are spot on). I've got my criticisms, of course, and the stories are somewhat hit or miss, but the good ones are pretty good - especially the final two-parter (the lady who plays the Romulan Commander is a dead ringer for the original) and I liked how the very end begins to tie into the start of the movie franchise.
I've heard about "Star Trek Continues", but I haven't seen it yet. I've been trying to find time to binge watch all of the episodes, but I just haven't found the time yet.