Michael over at the RKBArms Blog asked the same question recently. You can see his personal answers there.
First, let me say that I really think the question is almost invalid, especially to a law abiding American. On the one hand, the anti-gun crown will answer "zero," which just leads to a pointless discussion.
On the other hand, it's almost like asking how much money I need, or how many pages long should a resume be*. There is no real answer, or at best, any answers depend strongly on the assumptions that are made.
Here are the five essential guns Michael identified, which, given the nature of his blog, apply to a defense situation:
1. Every Day Carry
2. BUG (Back Up Gun)
3. Home Defense Sidearm
4. Home Defense Carbine
5. Home Defense Shotgun
I can't disagree with any of these from a defensive standpoint.
All I would add would be the caveat that there should be enough additions for each able bodied shooter in the household. In a SHTF situation, having a carbine and/or handgun for each person would make survival a lot more likely.
It also occurs to me that, depending on the size and layout of the house or area being defended, the number of Back-up Guns may need to increase.
For me, my guns are
1. Glock 21SF
2. Glock 19
3. Glock 17
4. SKS with detachable magazines
5. Mossberg 500
Admittedly, I sometimes carry the Glock 19 in lieu of the Glock 21, depending on my clothing choices.
In a SHTF situation, I would carry the G21 and SKS, my wife would carry the G17, and my son would carry a Ruger 10/22 with 4 - 30 round magazines.
The key here is making sure everyone is proficient with their assigned guns, and knows where spare ammo, holsters, etc. are stored. Then train, train, train.
On the gripping had, this list touches addresses defense needs only. One could make any number of lists based on the category in question:
Competition: One for each competition type and class. Skeet gun, trap gun. 3-gun rifle, Camp Perry rifle. SASS: 2 pistols, a rifle in pistol caliber, and a shotgun. (That's by far the easiest. Maybe.)
Hunting: Big game, small game, medium game.
Then there is collecting.
* On the issue of how many pages a resume should be, most people will respond one of two ways: either the resume should be all one page to make it easier to read, or the resume should be as many pages as it takes to convey the amount of information to get an interview.
But, in fact, this is a trick question: there is no answer any more, and here's why. Most resumes will never be printed on paper, they will only be viewed and read on a computer screen. So, since there are no pages, the question is invalid.
I suppose I would go with the second answer at that point - include everything you need to include so you get the interview. Remember, no one hires your resume, they hire the person, after an interview.
Disclosure: I work as an engineering recruiter, to pay for ammo and match fees.