Interesting that so many of you think you'd be going somewhere. I live way out in the country and my issue would be people coming here. Ammo would be my first consideration. We already have the shotgun and a couple nearly harmless guns for shooting squirrels. I found a four-foot iron pipe in the woods just this week. Rust or not, it'll be good for some whacking. Guess I should keep it instead of recycling it.
Next what I'd want would be solar cells on my roof and an inverter (I think that's what it's called) so I could use all my electricity myself and be detached from the (likely nonworking) grid. Alas, I've never made the investment in solar. We'd have to start using our forest for firewood. We'd run out in a couple of years, maybe, but by then we'd have run out of ammo and we'd be dead, anyway. We're only 100 miles from a major city and even though someone will conveniently blow up the bridges and make it harder for people to get across, 100 miles just isn't that far. The people living west of us in the mountainous regions will probably be able to hold out against incursions and they're better at living off the land. I hear possums make very good eating, and there are wild turkeys, bears, and deer. Lots of deer.
I find this all very silly, but on a morning when I'm not in the mood to buckle down and work, it's entertainment.
This.
I'm in the country too, and people coming here would be a big concern for me as well. Like Anarchist said, being out in the sticks could mean a few men being able to take my home, but I'd rather take my chances than live in a highly populated area. We currently have rain tanks and a creek fed dam, and I grow some of my own veges and herbs. Chickens are next on the list too. My main issue is that I'm renting my house from family atm, and there's only so much I can do until I buy my own property. Whether there is some sort of apocalyptic event or not, I have an interest in self-sufficiency regardless, so I have plans for when I can build my own place.
Solar panels will be high on the list, as well as a backup such as wind turbine. We're in a valley and get high winds here. The biggest issue I see is not with generating energy, but with storing it. Batteries don't come cheap.
I really like the concept of the Earthship houses, and want to utilise some of those aspects, such as lots of north-facing windows (we're in the southern hemisphere), walls made from materials that create thermal mass, maybe building into a hillside to utilise the cooler temperatures in the earth for air conditioning, and sunroom areas to grow food indoors. If I needed extra heating I'd probably be thinking a masonry fireplace, there's plenty of bush around and I'd be seeking a property that can supply tons of firewood. I love the concept of reusing water in the earthship design, but our council won't allow it.
Guns would be an issue for me. I would definitely want one, but they aren't legal in Australia unless you have a license and a genuine need for one, like if you are a farmer. Having said that, some of my neighbours have them, so it may be easier than I think. I've thought about joining a gun club nearby and seeing what options I have to learn to shoot, but not sure.
My ideal situation in an apocalyptic event would be that I'm already set up to be pretty self-sufficient so there would be minimal disruption, and having the means to protect myself. I struggle with the idea of raising animals to slaughter or killing kangaroos, but if it became a matter of survival then I would do it. I have lots of ideas and little things I've been meaning to play with (I was going to build a solar heater and a sun oven this past winter and never quite got to it), and it all sounds great in theory, but I think the reality would be far harder. Nevertheless it's a topic I love, and I think it's doable.