If you play the game Fallout New Vegas, at one point you have your brain removed. Later in the game you can even talk to your brain, which for some reason is a bit reluctant to go back into your body. But then, the Fallout series is based on cheesy 1950s style sci fi, and it’s not exactly known for realistic biology or physics. 
Anyway, there is actually a GQ question buried under all of this.
What exactly do you mean by this?
Your heart can actually beat on its own. What it can’t do on its own is adjust its rhythm for things like pumping more when you are exerting yourself. But basically your heart makes its own rhythm, and the brain only tells it to go faster or slower (that’s oversimplifying a bit but it’s the general idea of it). Without the brain connected to the heart, you end up with a low heart rate and low blood pressure, something that people who get heart transplants have to deal with.
The respiratory center of your brain controls your breathing, and unlike the heart, without a functioning brain, you won’t breathe. So if you mean you were breathing ok and then your brain suddenly somehow goes poof, then you stop breathing at that point.
We’ll assume some kind of message board magic that keeps you breathing to continue your hypothetical here.
Without a brain, you also lose some of your ability to regulate your body’s temperature. You won’t sweat or get goosebumps.
I think the rest of your organs will mostly continue to work. People with spinal cord injuries need to be moved around periodically or they develop bed sores and/or blood clots. Christopher Reeve developed an infection from a bed sore and eventually died from complications related to it.