I had a Quantum Fireball back in 2001 when they were the shiznit and it had a 3 year warranty. I want to say it was the 18GB, but it may have been an 8GB. I had it for close to two years, and it died. I didn't have to provide proof of purchase or anything. I just entered the serial number through their automated website, got an RMA number, and a few days later received a new hard drive. I immediately sent back the old one and had no issues.
The computer I just replaced I built back in 2000. Would I have documentation proving where I bought the parts, or even receipts? No. Would the manufacturer replace it if it was still under warranty? Probably. Although, the only thing left that would be under warranty would be the hard drive. Mainboards have like a year. Processors have like 7 days to 1 year depending on how you bought it (mine would only have had 30 days). The RAM may have had a month warranty. The video card has been replaced 4 times, and never due to failure. And, I still have the same sound blaster live platinum I bought 5 years ago.