I saw the British touring version of Les Miserables back in May and the use of video was fantastic - the fact that the projections were based on Victor Hugo's original drawings helped! I'm always dubious when anyone says that they want to use projection in a show, as I've seen it used very badly as well as very well.
I did a gig with the Sydney Dance Company last year where they used video brilliantly - they projected onto a green "slash" curtain (backed with a smother) which looked amazing - accompanied by a banging soundtrack, and then projected static backdrops onto the cyc - but they had done it properly, spent the money and had the proper gear to make it work! I also worked on a show last year about two retired couples travelling around Italy, and to cover scene changes the director had the idea of getting people's holiday video footage of Venice, Rome and a couple of other places, and our video designer created montages out of them all. It was a nice idea and actually worked pretty well (we put an appeal in the city paper for footage, and people were more than happy to give it to us!) - it set the scene nicely.
On the flip side, we did a show a little while back where the set was a grey box with no front or back; the back was a white cyc which the set designer wanted to project different images onto for different locations. Getting the footage was no problem, but projecting it was a whole other kettle of fish. We couldn't rear-project as the cyc was virtually on the back wall, and front-projection was very problematic as it would have hit the actors before the cyc, creating nasty shadows. So we spent a fortune on a short-throw projector, but even with it we still couldn't get a large enough image that was completely in focus, as even the short-throw wasn't designed to project an image as big as we wanted it. It didn't look wonderful, and it also created huge problems for the lighting designer as he had been forced to bring his frontlight in very flat, because of the roof on the set, and of course it then spilled onto the projection screen, causing problems with the visibility of the projections. All in all it was not a good experience, and looked far from good.
I go onto a production of Cabaret in a few weeks, and I know the lighting designer (who is also a video designer) is planning to use a projector coming in from either side - but he wants them as a lighting effect (beams in the air and effects on the floor) and not to project specific images. He's planned for this right from the word go and I think it'll be absolutely fine, because it's integrated with his lighting design and the show, and not a bolt-on "solution" for a problem caused by the set designer.
Operation of video can also be problematic - for years we've been running off DVD players, which I hate, but we haven't had the budget for a better solution. Recently we got some funding to buy Arkaos and a laptop to run it off, so now our video is triggered off the lighting desk, which has made all the difference in the world! I operated a show earlier this year where we had two video sequences (in the script - the characters made a couple of short videos which the audience then see) and we actually ended up running them off VHS! The show was set in 1995, and the video designer was busy degrading his footage so that it would look like it was running off VHS, when it suddenly struck him that we could just run it off a VHS which would make everybody's life easier! And I have to say, it was a breeze to operate; when you hit PLAY on a DVD it spins the disc up, thinks a bit, then plays the track, so you have to pre-cue it then pause it and hope that you did it late enough that it won't stop, having been on pause for too long; with a VHS you hit PLAY, the tape rolls and it starts instantly! It was dead easy to cue up - I'd just run the tape through to the right time, then hit STOP - no faffing with the pause button!