Radarscope shows the rain that is presently falling as well as other data that meteorologist use. The data comes from the NWS network of radars. The data is usually nearly live to 6-10 minutes old. There is no actual live radar as they have to make a sweep of the area. But it is accurate.
Rainfall accumulations are not very accurate IMO. They have a couple of products but the data isn't exact. It does give you an idea of what area received the highest concentration of rainfall.
Radarscope is the app used by most storm chasers.
http://radarscope.tv
Actual rain fallen needs a source of live reporters. There is an app called rain gauge. I haven't used it so I have no clue how accurate it is.
I don't care about the total rainfall. I want to know where it is raining in relationship to me or to where I am headed.