I've caught rainbows and kokanee on circle hooks - while trolling homemade crawler harnesses or my version of a wedding ring. With circle hooks I've always had a fish lip hooked. Though I've been told that circle hooks aren't for trolling - only for bait fishing (sometimes I just don't listen)
You might also try True Turn plastic worm hooks if you're fishing with crawlers. I've had them go a little deeper but not completely swallowed most of the time and less mortality on trout than a baitholder.
I agree with both RK and Walleye Seeker on toothy critters. When the bite is light, I've actually found them to be an advantage. Capthook and I were fishing Lake Mac from shore earlier this year. Total of four rods between the two of us right next to each other. He was using baitholders and I was using circles. I bagged four walleye to his one sucker (not trying to rub it in) and I think it mostly had to do with the fact that the bite was light and the fish weren't that aggressive. If the fish isn't that aggressive, he'll pick up the bait and turn to swim away in which case the hook embeds itself. I haven't had the issue where teeth became a factor - my biggest walleye at a little over ten pounds was caught on a homemade crawler harness with circle hooks.
I have had issues with larger catfish and small circle hooks where the hook tends to embed itself more like a lip ring on a human. Still got the fish in the boat but I was surprised it didn't come off.