Fortune favors the prepared...
I've given considerable thought over the years to how to secure a structure, and one basic fact keeps cropping up:
Most of the ways you gain entrance to a house these days, whether you're a criminal or a cop, exploit one or more weaknesses common to houses in the U.S., rather than simply applying overpowering force. That door jamb thing in the first post of the thread is an example of this. Armoring a specific weakness in common residential door technology.
But if you're willing to put in some work, you can produce some interesting alternatives to the standard tech. For example, I once read about a guy who was targeted by home invasion robbers who literally drove a car through his front door to get inside. When he rebuilt the front of his house, he put in some VERY hefty frame reinforcements and mounted the front door section on truck leaf springs. The next time someone tries to drive through that door, they'll BOUNCE.
Most of the weaknesses in a conventional door don't apply to a pocket door. Especially one made of solid steel. You can even leave the doorknob in place; It either ends up as just a convenient handle to slide the door open with, or can actuate the locking bolts that hold the door shut. Properly designed, such a pocket door might actually be easier to open than a conventional security door. And if it overlaps the top, bottom and sides of the doorway by, say, six to twelve inches, and the door frame is suitably sturdy, an attacker might not get through it even with a ram mounted on a police APC.
There's a company in Florida that sells shatterproof windows, their commercials involve bowling balls and hard impacts. That same technology would prevent someone from entering your home through a broken window (or throwing bombs through a gap).
Aluminum (or steel) siding and either terra cotta or slate roof tiles can do wonders for exterior armor. Neither will stop bullets, but they can add some fire resistance, and a layer of plexi-glass or lexan underneath IS bulletproof. An automatic fire extinguishing system built into the eaves drastically improves the fire resistance.
You can get chain link fencing that follows military or prison specifications. Difficult to climb, hard to cut, very sturdy overall. Put that on the outer edge of your property, high enough to stop someone from hurdling it, and your perimeter becomes a lot less porous. Put some nice lattice-work trellis fences and climbing ivy on the outside, and it becomes a lot more visually attractive. The trellis-fences can be part of the defenses too, build them flimsy so any attempt to climb over (even with a ladder) will break them, with simple line-break electrical sensors built in. A cat or raccoon won't trip the alarm, but anything from kid size up will. And when the alarm goes off, start an audio/visual security camera system automatically. Even if it's the police, they will claim in their reports that they identified themselves whether they actually did or not. Having video to prove they didn't can save your ass. And if it's not police breaking in, you have proof your use of force in defense of your home was justified. If you're paranoid, have a publicly visible recorder and one (or more) hidden in hard to reach spots, with simultaneous recording; Cast into the foundation with a USB port hidden in a light fixture is probably overkill, but you never know. Videos showing police misconduct disappear all the time, after all.
For more vigorous incursions, you can build a moat. Say, about five feet across, about four feet deep, concrete-lined, with a sloping outer wall and a vertical inner one. Keep the water chlorinated and circulating to prevent mosquitoes, maybe put in some decorative artificial plants. If you heat it, you could even use it as an oddly-shaped swimming pool. And those dimensions aren't exactly arbitrary...they rather resemble a different sort of structure the Army is rather fond of...purely by coincidence, you understand.
On a related note, you can put statuary in your yard. Dig a four foot deep hole, drop in a steel I-beam, surround it with tastefully ornamental cedar planks, and fill the gap with concrete. Set statutes, gazing spheres, potted plants, small fountains or what-have-you on the top of the post. Scatter them in staggered formation, about three or four feet apart (think of the five pips side of a pair of dice). Yes, this is paranoia talking, but even paranoids have enemies, heh.
Put all of that together with some exterior floodlights, and you get something that ought to keep out the average street gang or police for 12+ hours...the national guard for an hour or two, or the 101st airborne for about 5 minutes...
Just imagine, the first sign you have that the SWAT team would like to have a word with you, could be turning on the news during your leisurely breakfast, and discovering the "standoff"...