My strategy for surviving the zombie hordes is sort of layered in with my overarching survival strategy for when the world goes to **** and I have to get the heck out of dodge.
Basically I'm putting together a three tier survival kit, starting with a basic 24-72 hour 'constant carry' kit about the size of an altoids tin, excluding the Leatherman Tool and pen light I always have on me. In this you want means of water collection/decontamination (chlorine tabs and a plastic bag container), a way to gather food (fishing hooks and line), make fire, and some sort of shelter. A length of parachute cord and a black trash bag suffice for this as a last resort, which is what the kit is. You also have a tiny copy of the plant edibility test. Actually, you can check it out here, it's a really fun project:
http://www.survival.com/best.htm
After that is a 'Bailout Bag', which will be in my car at all times, containing supplies for a somewhat prolonged survival period and tools to be able to survive a bit longer. This includes more formidable shelter, basic tools (camp axe, shovel), more ways to get food (snare wire, a firearm where legal, a proper plant ID book), and a sufficient supply of ready-made food.
These two things are actually incredibly pertinent for ANY person to have, regardless of their opinions on doomsday. You could be out hiking and get lost/separated or injured. You could get stranded in the middle of a road trip. And as we've seen in New Orleans and many other places, natural disasters occur which necessitate not only survival capability, but -mobile- survival capability. More on that in a minute.
The final layer of my survival equipment is the 'INCH' Bag, or 'Im Never Coming Home' Bag. This is a larger supplement containing proper clothing, a few more tools and reference materials for long-term self sufficiency, additional rations, ammunition, and more redundancy; Two is One, One is None. It will also contain a hearty tent and sub-zero sleeping bag and an adequate first-aid kit; thank you, ambulance service, for being so zealous about pulling expired equipment off of the ambulance and not caring what happens to it

Finally, I'll have a few devices to make life easier and more bearable, ie an mp3 player, rechargable flashlights etc., and a solar battery charger with spare rechargable batteries. Ideally, money allowing, I'll have a FLIR camera (Forward Looking Infrared), which will help level the playing field against....anybody else with high tech equipment who wants to hunt me down. *cough*
On top of all of this, it's a good idea to have some backup copies of 'who you are' on a thumb drive safely socked away. ID documents, licenses and certifications, diplomas, photos, all of it. You may need to prove it some day. I'll have one of these as well as a small stock of barterables, ie silver and salt, as room and weight allow.
My actual strategy, for any survival situation, is to be very mobile. I am not against taking refuge somewhere, in fact against zombies I would be more willing to hole up than against a more sentient force. But my criteria for abandoning shelter is extremely liberal

IE, if I know that the town 20 miles south has just been infected (or invaded by an armed force), Brian is packing his rifle and going cross country. I'm probably not waiting for the first zombie or Commie Invaders to traipse up my driveway. Traffic permitting, I will take my car as far North and East as possible, hide it on some back mountain road or clearing, and ditch it. From there I will put as much distance as I can between myself and civilization. I'll establish a camp site and begin gathering food. Hopefully, before the first winter, I will have a more permanent shelter built. My main idea is to dig in to a well-drained, well-concealed mountainside and do my best to conceal the entrance. This will provide adequate insulation from the elements, yet should hopefully conceal my visual and thermal signatures from observing hostiles.
Something I'd like to toy with after I get all my gear taken care of is the idea of buried supply caches, and the idea of international refuge arrangements. I'm a few days hike from the Canadian border. I'd seriously like to meet a woman in Canada to have an arranged 'immigration marriage' with in the case of me needing to bail. Obviously it would only last as long as necessary and I would compensate her after getting myself established.
In a zombie situation, I would be more open to the idea of getting closer to the urban centers after the first 'lump sum' of infected began to die off (unless we have a more exotic sort of zombie that does not die and has to rot away). From the right base of operations in the wilderness, I would be able to scavenge from these areas and have it a bit easier, perhaps one day setting up base in the city itself. However other survivors are more of something to avoid than something to look for, in my eyes, unless I find an established city-fortress of survivors living as collective. My survivor policy starts with distant Observation, after which will come the Kill or Contact decision. For all I know, these people are cannibals, robbers, or both. Better safe than sorry.
One of my biggest concerns right now is what sort of armament to carry. I for sure want a side arm and a rifle. I would like to have a shotgun but in most cases it's too much extra weight for too little benefit. My difficult decision lies in whether to carry my semi-auto scoped .30-06 and go for long range engagements, or to carry a (possibly scoped) AR-15 which I can have my buddy build for me. Even a short, pistol-grip twelve gauge would be nice though for quick defense. One of my biggest fears is being asleep and suddenly being assailed by a grizzly. It's one thing to have to grab my rifle, hope I made it ready to fire the night before and then aim for something vital; it's another to grab the shotgun, whip it up and fire a quick succession of Slug, Buckshot, Slug, Buckshot. What's that, Bear? You're staying for dinner?
...Yeah, if you see me out there in the post-apocalyptic wasteland, just shoot me. I'm unstable and paranoid and I will kill you for your stuff.