I know this is a stupid question, but I can't find the answer anywhere. I'll be playing a game, and build no units, settle no cities, nothing. Then, when I end my turn, I'll go from +1 gp to -1 gp. So I check it, and my civic cost went up. I didn't change civics, so what's the deal? Is this a glitch?

civic costs rise as the game goes on - this is kind of like the inflation concept, that things cost more later on. unless you are playing your first game, I'm sure you've noticed that civics might cost a few gold in the first turns of the game, then in the 1900s you will see they cost hundreds of gold... just check the financial advisor screen, it's there for a reason so you can track all your costs in one place

Nah, I'm pretty sure that civic costs only increase with population increases. What you may have suffered is probably an increase in population of a few cities (you didn't mention that none of your cities grew).

Perhaps you move units from your land to others, and so rise the maintenance cost.
It's best to look at F2 at the right side, there you can see the costs of the turn