Best digital camera under Digital SLR. With clear picture and video capabilities?

I love the quality of pictures that can be achieved with Digital SLRs but I don't want such a bulky camera, just something I can stick in my purse that won't actually take up the entire thing, so I'm wondering what would be a good camera that has video capabilities? Not too concerned about prices. My dad recently purchased a cheaper Canon point and shoot and it takes way better pictures than any of my two previous Olympus cameras. I don't know much about what features to look for but I am leaning towards the Canon brand. Your thoughts?