Oh, I absolutely put a lot of thought into my covers. It's important if you want to sell your work! I admit I might overthink some of them though...
Since I print my comic, I do both issue covers (about 40 pages) and volume covers (200 pages, paperback book). With the issue covers, I can get away with just doing a single character and keeping it simple. They still look good but it doesn't tell you much about the series.
Then there's the volume cover that compiled all 4 of these issues:
I wanted to communicate a lot more about the situation in the story, focus on the character that had the most development, and instill a sense of unease with the looming threat she doesn't notice yet.
Volume covers always take me longer than I think. I struggled a lot trying to figure out a concept with this one and finding an interesting composition... the lighting was hard to pull off too and it just had a lot of effects. And part of me still favors the issue covers a little because they're more relaxed 
I feel like it's important to touch on character, world, AND story in a cover when possible though, so it's something I'll keep striving for and I hope I can get better/faster at it.