Had some problems last week with a three-legged cat. I came home one night to find the cat asleep on my sofa. I was baffled as to how he had got in and as soon as I saw him, he immediately hid under my sofa. I managed to coax him out with tuna and put him outside.
The next day, I came home from work only to find the cat looking out at me from my windowsill. I had no idea how he'd managed to get back in. I suspect he'd used the fabled 'catspace', a gap between the fabric of reality that allows cats to get into places they're not allowed to or to suddenly disappear without trace from right under your eyes.
Once again I coaxed him out with tuna and put him outside. He then leapt straight through my bathroom window and hid again under my sofa. I tried once again to lure him out with tuna, but he'd obviously wisened up to the fact that this would mean I'd throw him out, and remained securely hidden under the sofa.
I decided I needed to change tact and tried to get him from under the sofa with a broom. He did come out, but only to hide under my armchair. Further broom persuasion only succeeding in making him hide under my woodburner. I tried squirting him with water, but he simply refused to budge.
After a fruitless hour of trying to get him out, I ended up having to put on a leather coat and gloves and grab him by the scruff of his neck to get him out. (It was at this point incidentally, that I realised he only had three legs).
The next day I found him still in my back courtyard and realised he was unable to get out - he'd fallen off the wall and couldn't make the jump. Fortunately my neighbour knew who's cat it was and I was able to alert the owners that their cat was stuck in my garden. He came round and the cat leapt onto his shoulders. He left my house like some kind of cheap pirate.