Why are some of my circuits not working?
It looks like you lost one of the hot legs to your service. It could be a bad connection on your main breaker, a bad connection in the meter base (had this exact same thing happen at my church's parsonage...an old house with very old electrical), or a bad connection at the transformer, or the overhead (assuming you have an overhead feed) connections to the triplex from the transformer to the wires at the weather head.
Loose connections can be very confounding...when they heat up, they lose connection or provide a very poor connection. Then they cool down and make a somewhat better connection...for a while!
You should get the power company involved to at least see if there are no issues with the supply.   If not, then proceed to trace down the problem using a multi meter, starting with the main breaker.   Be careful!  You'll be dealing with REAL POWER there. PPE and rubber gloves that are certified for electrical work would make you pretty safe, but still....PPE is needed, esp. goggles.