One thing that always catches me off guard especially early on is if the AI change trade routes and stop coming to you. Often times your left wondering why you were running a marginal surplus and now your at a deficit. Also I could be wrong but I belive different era units have different maintenance costs so mass upgrades of your army can create a problem for you.
Also there's a couple social policies that can affect you. I forget the names but there's one in tradition that allows the troops that garrison in a city to be maintence free. If you decide to mass deploy a resting army, like in an invasion, you might suddenly see the maintenance of those units kick in.
A similar concept hahappens with a social policy in Honor. One of those gives you 1 happiness for units garrisoned their. Once they leave that city your happiness dips back down.
Finally of course your trade routes ending will show you a sudden drop income until you redeploy them. This may be common sense but I've done stupid things in playthroughs in which I might stop sending a lucrative trade route to a rich city and divert it to a city state for the mission bonus or for safety, but I take a hit in income. Also when 2 trade routes end at the sam time, especially during a war, I might put one to sleep to work on moving other units and forget to resend that trade route.
Oh extra one that I fall victim to alot is the city governors. I always micromanage them early in the game but as my cities get bigger I often forget them. So the city starta au to assigning citiZena and at first it may set them to gold tiles. But sometimes after making a building or a change in tech they may assign thor citizens to food or production tiles and might have assigned a group of citizens to specialist slots. This might create a deficit if multiple large cities do this. Avoid it by locking citizens into sensible tiles.
You can also remember that in hard times too. I've had early games where my budget was horrendous and the first thing I do if all my trade routes are static is assign mmy citizens to better gold tiles because early on growth is more important but if your broke but need a large army it might be smart to switch to gold for a short time
