I'd like to see a fan film set in the new universe. Either on the Enterprise or the Kelvin.
I know WB have let Nolanverse Batman films go ahead, and Doctor Who fans have done stuff based on the newer seasons, but strangely Bad Robot/Paramount/CBS have vetoed anything based on the JJVerse.
Someone mentioned the Tressaurian Intersection above, and I'd like to throw in a mention to the German Original Series/Next Generation crossover feature 'Das Vermachtnis' (The Legacy), as featured in Denise Crosby's Trekkies 2 documentary. It cold have been just incredible!
It featured well-tailored uniforms, Q, Klingons, plus great replicas of the original/-D bridge; TNG Shuttle and Klingon bridge. Picard looked younger but with hair, but that didn't matter. The whole thing just felt RIGHT. 'Vulcan' Willi Wiegand, a well-known Spock imperonator in Germany who was in charge of promotion, regularly corrosponded with fans online and provided updates.
There's a preview of what might have been at 2:53. I would have watched the entire thing without subtitles/dubbing, even though I don't know German. Apparantly the whole thing was shot, however Director Christoph Hees decided in post-production it was 'God's will' that the thing would never be completed. Such a damn pity.
Hopefully all the footage still exists so someday it could be edited/SFX etc. Hopefully. I tried emailing Christoph on Willi's advice but alas no reply.