My first build was back in 2000. I put together a budget 400 MHz K6-2 system for my wife's grandmother to replace her old P-133 system, out the whole thing togther, and booted it up only to find that there was a noticable jitter in the picture on my monitor, even on the BIOS and fdisk screens. Checked everything I could think of, but never could get a stable picture that didn't jitter. After I RMA's the board and reinstalled everything, only to find it was STILL doing it, I took the system over to a friend's house to see if he could figure out what was wrong, only to discover that the picture was rock-solid on HIS monitor (and later my wife's grandmother's monitor). Could never figure out what was wrong, since the monitor seemed to like every other video card I hooked it to.
All was fine, until I got a call a few weeks laster that her modem was out. It refused to connect, but when I reinstalled the driver it was all fine. I tried another cheap winmodem and it has issues connecting reliably to her ISP (it kept getting hung, and remained stuck sounding single annoying a high-pitched tone until you hard rebooted the machine. Finally, I got tired of fighting with the cheap $10 modems and bought her an OEM US Robotics controller-based modem out of my own money so she'd finally be able to get online without any hassle (and so I wouldn't have to run out there every week or so to fix whatever had gone wrong with the crappy winmodem). The system is still running without a hitch, although it has now been replaced as her primary machine by a AXP 2000+ based Shuttle XPC I built for her.
My second build was that Christmas, a PIII machine for my family that my uncle and I worked on together. My contribution was a GeForce 2 MX to make the 815E based machine into into a decent gamer. The only problem was that when it was installed, the games would crash a few minutes into playig them. After trying out updated drivers and multiple installs of Win 98, all I had left to try was the dread BIOS flash. First I tried Intel's windows BIOS flash utility, which locked up just as it started the flash (but luckily just before it had started reprogramming the chip). Once I tried it again, this time with a floppy, all was well in the world at last and the GeForce card was happily running MDK2 for hours.
At least until Windows 98 mysteriously began getting corrupted about every other week a few months later. My parents blamed my constant patching of Windows and upgrading of drivers, but for a while I never could really figure out what was wrong. I tried all sorts of combinations of drivers, but nothing ever kept the system running happily for more than a month. I got used to having to run over, format the drive and reinstall Windows. One day for chuckles, I killed and recreated the drive partitions and noticed it too about three tries for the hard drive to pass the integrity tests in fdisk before creating the partitions. After I got the system up and running, I downloaded the Mator drive utilities and discovered that the drive was dying on us, so off to RMA the drive went and things were finally well and good for a few years. That is, until my little brother moved the system into a new case without my assistance and neglected use the standoffs. The traces burned off the board quite nicely, I'm told.
The last major issue I had with a build was when built a Duron system for my wife's aunt and uncle and slapped in a brand new 20GB Western Digital hard drive without bothering to RTFM, which would have told me about the new "single drive" jumper setting they added to the drives in sometime after the 8GB WD drive I put in her grandmother's machine bad been made. I spent a good half an hour trying to discern why the hard drive only seemed to be noticed by the motherboard on every third boot or so, until I got around to actually reading the installation guide.