Most of them.
Your body continues to breathe, circulate blood, digest food, supply nutrients to organs, etc.
Notably the body also attempts to repair itself at a faster rate while asleep; and the brain switches modes as well.
The brains sleep mode moves the short term memories into the long term memory portions of the brain; if you happen to begin waking during one of these cycles your waking mind will interpret them as best it can (this is what dreams are, your waking mind viewing the movement of short to long term memories and the connections they are making in the mind)
Other body systems such as hearing and sight are also technically still working, but they are in a much more subdued state; but if they receive enough stimulation you will wake up; if they weren't on to some degree the stimulation would not wake you up.
About the only system that isn't at least partially functional while sleeping is the conscious mind.
Chat with our AI personalities
The body systems that are active during sleep include the respiratory system, which controls breathing, and the cardiovascular system, which controls the circulation of blood. The digestive system may also be active during sleep, as the body continues to process food and eliminate waste. The nervous system, which controls the body's responses to stimuli, is also active during sleep, as it plays a role in regulating the body's sleep-wake cycle. Additionally, the endocrine system, which produces and regulates hormones, may be active during sleep as it helps to regulate many important bodily functions.
When you sleep, your body is still working to maintain essential functions such as breathing and circulation. However, the most active part of your body during sleep is your brain. Your brain is responsible for regulating your sleep-wake cycle, and it also plays a role in consolidating memories and processing information from the day. This is why it's important to get enough quality sleep, as it allows your brain to perform these crucial functions.
While you're sleeping, your immune system releases a type of small proteins called cytokines. If you're sick or injured, these cytokines help your body fight inflammation, infection and trauma. Without enough sleep, your immune system might not be able to function at its best.
While dozing the respiratory, circulatory, stomach related, excretory, and nervous systems all work together. All these systems cycle through to help us sleep.