The only place that I've ever heard of that requires it is CompUSA's tech/repair lab (or was it Best Buy?). I took a hardware class a few semesters ago that focused largely on following the A+ study path, but I never really felt it justified in spending $145 for a test that nobody cared about to learn information that I'd never used. One of our test questions in the hardware class was "identify the pinouts of a PCI card slot". I mean, seriously, when are you ever going to use that? In real life, you take a PCI card, stick it in the slot like a Nintendo cartridge, and screw the backplate on. If a motherboard is fried, simply buy a new one; they're only $100 (compare that to getting it repaired!). And so on. Everything is so integrated now that there are very few things you personally can do to repair them without extensive training and tools. I've been working with computers seriously for over six years now and the only things I have in my toolbox are a screwdriver, a can of air spray for dust, and a USB stick with stuff like AdAware, Spybot, XP's Service Pack 2, etc. That's it.
The real kicker is experience. If you're not confidant with computers, buy an old junky PC off eBay and screw around with it. When it breaks, fix it. Computers are mostly about determination; you fix nearly anything, it just takes the patience to keep playing with it until it works. Nearly all of my knowledge comes from plain old experience; I've owned just about every computer widget you can imagine and now all I do to keep my knowledge current is read Anandtech and a few other computer news sites once in awhile. Once you've established the knowledge base of how computers work and you get a feel for how to run them, you're set for life because you can learn any new piece of hardware, software, or firmware very easily.
With all of that said, if you are interested in pursing an A+, then by all means get it. I'll probably get it eventually just for resume fodder and to increase my knowledge. Any knowledge you gain is a Good Thing, and the A+ study materials are excellent resources for learning all about hardware. One of the things I struggled with when I first started college was the way I learned things from books. Everything seemed so methodical and organized; the A+ book I had was well over a thousand pages and it seemed like I would never learn how to work on computers very well. I decided that I really wanted to learn how computers worked and so I spent tons of time and most of my paychecks on computer stuff, building my experience and having lots of fun along the way. In my opinion, that's the best way to do it. Just develop your passion and give it time; you're not going to become a computer guru overnight, there's just too much out there!