When the Zombies come, some experts believe that physical fitness will be key to escape and survival. When states were ranked on their ability to survive a Zombie Apocalypse, states that had more participation in fitness activities were ranked higher than states with couch potatoes. If you are at school, work, or Walmart, when Zombies show up, you'll need to be quick on your feet.
However, one alternative way to survive a Zombie apocalypse is to not go out of your house and fight with zombies. If you have enough food, chips, soda, and reading material stockpiled, you might be able to shelter in place. Typically sheltering in place is a recommendation by authorities when their is a chemical or biological pollutant that has been released into the atmosphere and it's dangerous to go outside. Here is an American Red Cross data sheet on how to shelter in place. In case of Zombies, staying inside probably beats running outside and fighting with them. If you've got the necessary supplies, you could just barricade yourself in and sit the whole Zombie apocalypse out. Of course, you'll need water. According to ready.gov, a person needs 3/4 of a gallon of water per day for drinking and another 1/4 gallon for sanitation. More is needed in hot climates. If Zombies are wandering animated corpses in various stages of decomposition, it stands to reason that the Zombie threat will simply bio-degrade eventually.
Of course, high cholesterol and hardened arteries might be a bigger threat than zombies. So, it would be prudent to be fit. Start slow and increase your physical activity. In the event of a catastrophe, the ability to run, jog, or even walk a few miles would be reassuring.