I know there are much smaller designs, much faster designs, and some more flexible designs, but I think this one has a place. It only has one brewing stand, so you have to wait the full brewing time from start to finish, but what I really like about it is the user interface:
Each dropper is how many items you have in store, and you can select which ones to add to your potion by flicking all the levers. You can add extra blaze powder and more water bottles further to the right, and that chest in the floor is the output. The lamp closest to the ceiling is a lamp indicator to tell you if you're out of something, and the button closest to the camera starts it. The lever right below that is if you want to automate the system, in which case it will keep brewing until you run out of items or shut if off. Everything you need to interact with is right here, which I like.
The circuitry is hideous, but here it is:
The red circuits are for item transport; the white, lime, and blue circuits comprise an emergency shut-off in case you run out of items or try to put in both redstone and glowstone, etc.; the green circuit is what automates the system if you pull the lever; the magenta circuit locks the water bottle input for when the completed potions are being taken out and unlocks the hopper minecart to take out the completed potions; the yellow circuit is the timer; and the orange circuit sets off the timer.