My first digital camera (a Minlta Dimage 7) had an electronic viewfinder and after using it for a couple of years I came to see some nice advantages. Not that I'm sold on the principle, but I can see plenty of reasons to spend R&D time and money in refining it.
At first, the smearing, stutter, time lag and lack of detail drove me crazy... but all of these are things that time and development have improved since the D7 was on the market... overall I'd say we still aren't there when compared to the best optical viewfinders, but you can see progress being made.
Power consumption is a concern too. Minolta tried to address this with a sensor next to the viewfinder that turned it on and off in response to the proximity of one's eye. I'm sure other solutions are out there as well so we may not have to worry about this at some point in the future.
I did like the fact that there was less vibration, no mirror blackout and no noise (in fact, the Minolta had to provide a soft click sound that you could turn on and off, otherwise you couldn't really be sure you'd taken a shot).
Another plus was the response to light... you could actually get a rough idea of exposure before you took the photo, and you could also see color shifts which would let you know if your white balance was correct. Also, you could turn on a low-light mode that would brighten the finder in a similar fashion to a night-vision scope... this came in pretty handy at times.
The most serious downside to the EVF for me was lack of detail. I have enough problems when focusing manually on the new DSLR's (the old split image and microprism aids in my film SLR's are sorely missed)... but the EVF was much worse, there was never enough detail there for critical focusing. Sure, some EVF's let you magnify a portion of the image just as you can with Live View on most DSLR's, but who the hack has the time to do that in most shooting situations? I think for most photographers, viewfinder detail is going to be the most critical sticking point of the EVF.
But I'm trying to keep an open mind... the EVF may end up being a great boon to photographers if manufacturers can address its current problems and make them more attractive by providing features our optical finders don't have (like the aforementioned magnification, as well as zebra and peaking).
For now, I'm sticking with my DSLR.