Point and shoot cameras seem to be in a dismal spot, with cameraphones eating at them from the bottom and digital SLR cameras pushing down on them from the top. However, think that they will have a strong niche for the foreseeable future. Their growth will probably slow, but they are far from extinct.
What's going to save them? Size, picture quality, and video.
Picture quality: Seems like an odd strength, given that it is much worse than a DSLR, but instead compare it to a cameraphone. Cameraphones have tiny sensors and tiny lenses, which means that they only take decent pictures in bright light. P&S cameras, with their larger sensors and better flash can take better pictures. Plus, the more advanced feature like face detection work better when you have more processing power to dedicate to them. And Zoom, how many camera phones have a 3x or 4x optical zoom?
Size: Seems like an odd strength too. They are much bulkier than a camera phone. You actually have to remember to take them with you instead of always having them around. However, compared to a DSLR, they are much, much smaller and lighter. You can put it in your pocket or bag without it being uncomfortable.
Video: Given that we are mostly talking about still cameras, video may seem like an odd strength, but really, it is the point and shoot camera's secret weapon. 5 years ago, they took 320x240 video at 15 frames a second without sound. Now almost all of them take 640x480 video at 30 fps with sound. That means that today's cameras take good enough video that you don't need a video camera for you 30 second to several minute clips. Where will they be in 5 years? Definitely taking HD video, probably at 1920x1080. For short videos they will be perfect. Longer ones will be fine, there will be plenty of flash memory, but I think they will compress things too heavily to do much editing, still, for most people, this will be all they need.