I've had some experience with LED's with one of the companies that I contract to do work for. I can tell you that in the last 3 years or so LED's are about ten times brighter than they used to be, for the same price. They are becomeing much more widely accepted and used, so every day we are seeing more and more configurations.
That being said, they put out a different type of like than incandescent, and it is very difficult to get the same look of an incandescent out of an array of LED's. The main problem is that they tend to have a very narrow beam (the cheap ones anyway), so they don't work with a reflector that you would use with a single incandescent light. One of the unique properties of an incandescent light is that it typically gives off light in all directions. To do something similar with LED's you would most likely have to aim the array backwards at a reflector, leaving a "hole" of no light where the back of the bulb (now facing you) is. You could possibly use two arrays back to back, but you start running out of depth quickly.
If you don't care whether it looks original or not, there are LED products out there that will do the job. There are also companies that will design a custom LED light for you if you send them the light you are trying to retrofit. As Paul said, they don't present enough load typically for a standard flasher to work, so you will have to get a special flasher for each independent flashing circuit. They run about $15 each.
I messed around with the idea of running a bunch of LED lights on my ambulance, but in the end I couldn't get them looking enough like original and tabled the idea for now. I may revisit it at some point, since there is new technology out there and it is getting cheaper and cheaper as they are used more widespread.