One of the oldest machines I've had was a Dell OptiPlex GX1 PIII 733. I purchased it used in 2003 and didn't replace it until a 2007 MB. My first Mac.

It was an early 2007 model and is my current laptop. I say replaced, but in fact I kept the Dell as I liked having a desktop machine around and finally took it out of service with a 2009 Mac Mini. That machine was short lived as I sold it and bought a 2012 Mac Mini 2.3 i7. There really was a speed difference between the two, but mostly it was that I couldn't Airplay mirror, which was important to me and I started to feel that all my computers were getting old at the same time. I use the laptop to take notes and though I'd like something slimmer, it's fine for what I need it for. It's running Lion, which is unsupported as of October, 2014. That's EOL as far as I'm concerned for it, but will probably wait for Skylake to get a new laptop or go used as performance isn't as much an issue as current OS support. I'm not sure how old the Dell was but the PIII 733 chip was released October 1999. Lets call it 2000.
2000 Dell PIII -- 9 years
2009 Mac Mini -- 3 years
2007 MB -- 7 years and counting; will probably be 8 years total
2012 Mac Mini -- will probably keep until unsupported
Back in the 90s machines really did go out of date fast, but these days, for most people, I think a 2 or 3 year replacement cycle is a little excessive. One could argue for replacing when the machine still has value and you'll never have an old machine.