Not something I found in my mouth, but something I put there. When my son was about six months old, I had to extract a bogey from his nose, and it turned out to be the stickiest item known to man. After several failed attempts to wipe it off onto my trousers and the carpet under the settee, I had no option but to try and eat it instead (well I probably did have other options, but I was watching telly at the time) .
It then turned out to be completely unswallwoable, as it had stuck to the roof of my mouth. In the end, I had to get up and get a tissue to wipe my mouth out with and chuck it in the bin.