Leading to my LARP thoughts, I was reading SciFi Now (a result of looking for something to read on the train down to Dragonmeet) because it had a few pages on Doctor Who fan films.
I've dabbled in the murky world of fan films before (writing a serial-numbers-filed-off Mage campaign comedy, dating someone who would later be the DoP of a Buffy fan series, giving ten bucks to the making of RVD2) and Doctor Who is a natural for the fan film treatment, since it already has a dozen Doctors so recasting the role isn't a deal-breaker, the classic series often had production values that anyone with a modern digital camera could better and the new series is almost entirely written by fans...
Among others, the article discusses the almost-legendary Devious (filmed while Jon Pertwee was around to make a guest appearance and still not finished), the impressive-looking but fallen-off-the-internet Millennium Trap, Sylvester McCoy and Sophie Aldred in Gene Genius and the oft-times clever but overly ambitious new-series-alike Doctor Who 2009 (I say overly ambitious because it's late 2010 and the second story isn't online yet).
Puzzlingly, presumably to only include things theoretically readily available on the net, it doesn't mention Mark Gatiss's P.R.O.B.E. series of videos, which are a fairly important part of the gap between the classic and new series, I'd say.
It also doesn't touch on some great things I've found myself on the YouTube, like Restoration of the Daleks or The Hitchhiker's Guide To The Daleks. Or as directed by SFX, Doctor Who 2001 - A Who Odyssey.
As well as amusement value, some of these have swipeable imagery and ideas.
I would of course love to grab some actors and some of the above effects guys and make one myself, but that way madness lies.