No Armageddon plans here (not really), but I do keep plenty of spares for many of my bikes on hand. I live over 20 miles from the nearest LBS. We live a bit off the beaten path so we always try to keep plenty of things on hand.
As far as using the bike to outrun the zombies...I have used my bike(s) to my advantage after a couple of hurricanes, specifically Fran in '97 and Katrina in '05. During Fran I was in Fayetteville, NC the neighborhood I lived in was completely cut off due to massive trees down across all the roads in the area. I was able to move about freely on my MTB/Commuter. During Katrina I was Jacksonville, FL where I had evacuated to from Mobile, AL. I was back in Mobile within 2 days. The biggest problem was a fuel shortage. Many of my coworkers were spending every other day in gas lines for up to 4 hours to get 5 gallons of gas. Me? I had stocked up on fuel prior to the hurricane, and had brought my bicycle along. I parked the truck and road my bicycle to and from work.
FWIW I usually take my bike with me when I go to out of town job sites, people always ask me why...I tell them it is my dingy/lifeboat.

In the US we are seldom more than a day or two away from a gas shortage. I keep my truck tanks at least half full or if working way out of town, I keep them full. If the crap hits the fan I will head for home ASAP, drive as far as I can and cycle the rest of the way. Of course I live right next to a huge military base that probably would be on the primary target list. So if that is the flavor of Armageddon it probably would be pointless to head home.
Aaron