We got a free 1 year home warranty when we bought our house. When the a/c went out, they wanted to replace it with another small unit like we had. We opted to not use the home warranty and buy our own larger, better unit. It lasted for years and we use our a/c almost year round here. Needless to say, we didn't renew the home warranty.
We have had some large expenses like repiping the entire house, but the home warranty wouldn't have covered that anyway. They would have just paid to fix the leaks. I'm not sure it would even have paid to fix the walls and ceiling affected.
I'm really picky about having things done right and don't have that option with a home warranty. If you decided not to renew, put that money (and hopefully a little more) in an account so that you will have something to fall back on in case of something breaking.