If the massive infrastructure grid that keeps our modern world chugging along were to collapse, one of the first resources to go would be gasoline and diesel fuel. You may be able to scrounge up a small amount, barter for some, or if you're really prepared, maybe make a limited quantity for yourself. But, essentially, you'll have a tank or two of gasoline for your vehicles and that's it--once you're out, that's it.
One of the alternatives that people often think of is the good ol' horse. I actually had the opportunity to ride a horse today -- a short guided ride -- and let me say, this option is best left to the experts. Someone who owns horses, rides them on basically a daily basis, knows how to care for them and who has all of the necessary skills and infrastructure in place pre-TEOTWAWKI.
If you are already a skilled horsemen and understand how to take care of a horse, then they have some advantages. No fossils fuel required, off-road capable and they have better hearing than you or I do. They can pull wagons or basic farm equipment. They reproduce, giving you transportation and valuable barter for years to come. And, if you're starving, they're a good source of protein.
I've ridden horses before, but it's been a while, an after about an hour in the saddle, I was done for. Sore and exhausted--my body is just not used to riding a horse. My horsemanship skills are non-existent, and my knowledge of horse care, tack and saddles, etc. is basically limited to what I've seen on TV or read in books. Horses are also quite expensive to own and maintain - essentially a major lifestyle choice. I probably won't be riding on Silver when TEOTWAWKI rolls around, and most of you probably won't either.
So, what else then? Let's look at the third world, where poverty and limited resources are a fact of life. What do they ride around on? Small mopeds and bicycles. Both are easily maintained with basic handtools and spare parts, and both can go over some fairly rough terrain. Both also require fairly simple and common skills to drive around. They can also carry a fair amount of cargo; you've all seen the pictures of 3rd world bicycles piled with a ridiculous amount of stuff.
While many mopeds require fuels to run on, they get very high MPG, getting you further out with your limited fuel supplies. And there are more and more electric mopeds and scooters coming on the market; if you have a solar system at your home or retreat, this could be an ideal option. Many of these are actually quite inexpensive, though made overseas and probably of hit-or-miss quality.
Bicycles have long been touted for their post-TEOTWAWKI uses; the Viet Cong are often cited as an example of the utility of the simple bike--they used them to move equipment and weapons all through the jungles of 'Nam. Most of you probably know how to ride a bike, and for routine errand running, a bike is probably the ideal for most people. Gets you there reasonably quickly, gives you some exercise and burns only calories, and used bikes can be had for dirt cheap at garage sales, Craig's List and such. Even if you're like me and have zero interest in cycling or mountain biking, it's probably a good idea to a couple decent bicycles around.
Finally, there's your built in transportation--your feet! Don't overlook the importance of having quality shoes and boots around, plus backups! Unless you have abo-feet like Cody Lundin, you'll be nigh-useless without good footwear.