I had an L&C power supply, 300W, running a system with an AMD T-bird 1GHz, and 4 IDE devices. Well, I also OC'd the Tbird to 1.4GHz. Now, the high-end Thunderbirds were very power hungry, like up to 72W for te 1.4 I believe. Well, this thing was running slightly increased voltage, and doing 1.4GHz. I ran the CPUBurn utility to stress the processor. A few seconds into the test, the system shut down, and I smelled the strangely familiar odor of fried electronics. I opened up the power supply and saw a lightly singed place on the circuit board. A component or two had apparently been overloaded when the CPU was stressed, so instead of shutting down like a good PSU should do when it's overloaded, this one just let its components fry themselves. The system was fine, but of course the power supply was dead.
Still, I'd say, yes, use generic ones, ONLY if the system is significantly below the rated output of the power supply, like maybe a socket 7 system, or a real basic socket A or Pentium III computer - budget videocard, 1 hard drive, 1 optical drive, not much else. And make sure whoever's using the computer knows to upgrade their power supply next time But a fully loaded system, no way. If you can afford good components, get a good power supply to go with it.
My main system is using a 420W TTGI (never heard of them, but the supply seems quite good) PSU. Nice, long cables, plenty of connectors, and it's running a lot of hungry hardware; heck, rather than re-typing the components, here's the links:
Main system
Secondary system (uses an Antec Truepower 430W, after a generic 400W proved to be insufficient)