If power goes out, will my phone still work?

It depends on the type of phone you have. "Corded" phones require no electricity and plug into the wall jack. These phones should not be affected by power outages. Most "cordless" phones require a base station plugged into an electrical outlet. The base station transmits telephone signals wirelessly to each hand held phone. If there is no power to the base station, the phone will not receive telephone signals.
Cell phones will work as the tower has back up batteries. If you are one of the 52 % that does not have a cell phone you can plug in a corded phone either a dial phone or a touch tone. These types of phones do not get their power from house current, so they will work fine. You say you don't have a corded phone, well they are very low priced so get one. I have two that I keep in a closet just in case. By the way when the cell phones are overloaded or the batteries run down they don't work either. eBay is a good place to get an old dial phone. Just do a search for "dial phone".