I like to scrub soap scrum (Oh which I have an ample supply at all times >.> go hard water!) out with a soft-ish dollar store toothbrush. Rinse it off with hot water, shake as dry as possible and put on a stand to dry. If I feel like it needs to be sanitized, I hit it with some barbicide after this.
I can't speak on Gillette-style DE's that have more parts, I use a slant. I've noticed that it does get build-up on it. I find it easier (by far) to do bi-weekly short cleanings than to let it go. I simply use hot water and a bit of soft scrub and get fine results. Getting into the comb is a pain, hence the frequency of my cleanings.
Does anybody else use baking soda toothpaste to clean there razors? I do because we have always used it to clean jewelry based on advice from a jeweler. Do anyone see a problem with this I just put some on an old toothbrush and go to town. Seems like this would be less harmful that scrubbing bubbles and has no toxic chemicals in it.