I've had my Apple //e for a few weeks; the first day I had it, the power supply catastrophically self-destructed. By that I mean one of the uber-fun paper AC filter capacitors blew, leaking out burning icky gook. I had to clean that off of the PCB eventually (or I just thought about it for a while, decided it wouldn't short anything out anytime soon (hopefully), and forgot about it). Yay.
I was in the garage writing some BASIC programs on my //e and heard a hissing noise; I thought for some reason that there was a snake or lizard in the garage, so I turned my back to the computer for a look around, only to turn back to the PC and find smoke coming out of it. Not a great sight. My garage smelled of burnt marshmallows for days. However, luckily, the computer was not damaged, and I wasn't worried because it continued functioning perfectly up to the moment I unplugged it, indicating that the cap's failure did not cause damage to the main motherboard and was not function-hindering.
Thus goes my adventure of replacing the old electrolytic capacitor in the Apple //e power supply, which is quite simple and an intriguing journey into a wonderful product's design.
The capacitor that broke, the rectangular 0.1uF RIFA, can be seen below. As I'm looking at the photos now, I can also see that when it burst it sprayed some dielectric fluid all over the inside of the PSU case—something I neglected to notice during my hours spent working on the unit. Someone is observant. Hope that doesn't short anything out!
You can see the photos of the power supply unit and capacitor once I took everything apart. eBay, my dearest friend, had the best price on cheap Chinese Class X2 0.1uF safety filter capacitors for the power supply. I could have replaced it with the same type (RIFA paper caps), but these are prone to failure. Luckily these caps don't play a huge role in the function of the PSU, and are simply to filter out noise in the AC for the most part. Only one burst, but the failure-proneness of old-style paper caps made me keen on the idea of replacing both with new polyester film capacitors. I got 5 of them for $5 from China. (I'm including the link knowing that any future reader might find it gone; sorry if this is the case).
However, I couldn't find any available that had the approximately 20mm lead spacing like the previous capacitors, so when I went to solder the new ones on I was happy to realize that the board has hole spacing for both nonstandard 20mm leads and 15mm regular leads like the ones I bought (I figured I would just somehow squish them onto the board with lots of globules of solder or something of the like). So that made my life easier.
I also enjoyed spending a while reassembling the PSU, since I had to desolder the power switch and 110v receptacle in order to maneuver the PCB out of the case. It only took me two tries to get it right (the first time, I put the receptacle on the INSIDE of the case, and when I pushed the 110v cable into it it just collapsed into the depths of the case. That kind of annoyed me since I had to resolder it all—the switch can only be removed outwards, since it has a lip over the edge of the case).
At some point I really need to get around to replacing ALL of the electrolytic capacitors in the power supply, which are also prone to failure over time as the electrolytic fluid that makes them work dries out. As soon as I get my new digital multimeter (I have a lame analogue one now) I suppose I'll test the caps I have to make sure they're all happy. As long as they don't fail, I have no problem with putting off a complete recap, but that'll probably be a good idea for the future. You can find some schematics for the power supply around the interwebs, though I tried and didn't have very much luck at getting any usable ones in the few minutes I spent surfing.
To summarize, the Apple //e power supply is robust, cool (not literally; to contradict my next point, the way the case was made is like an oven!), simply designed, and just plain awesome, but problems develop naturally with old capacitors and other electrical components over time, especially if they are in an incubator-like PSU and have a continual 110v running through them for hours on end. Therefore, if there is a problem with your Apple II PSU, it's probably a common and yet easy fix for someone with even basic electronics knowledge, so don't fret. The Internet is a great resource, but in this case just open it up and it's most likely a simple component replacement (as long as it didn't fry your motherboard!).
Let me know if you have questions, comments, or need assistance with anything!