Do it!!! It's awesome! Saves money, you get a high pitch rate and less cleanup.
I find that bottling is a perfect activity to occupy the time while you wait for the mash or boil. Not having to clean / sanitise the fermenter is an added bonus.
You don't have to make the same kind of beer, just something that uses the same yeast. People say that you should try to move upwards in gravity, ie brown ale -> porter -> wee heavy-> RIS not the other way around.
You will find that if you pitch the new wort on top of the old yeast it will be a huge overpitch. This isn't a big problem, but it's probably a better idea to remove 1/2 to 3/4 of the yeast/trub with a sanitised cup. You want to leave behind 2-3 cups, that will be plenty for a robust fermentation.
I plan my brew days around reusing the yeast as much as possible, it's so much easier than mucking around with starters, and cheaper than buying new yeast for each brew.