The practical minimum for a modern distro is probably a Core 2 Duo (2006). You will likely need a lightweight DE on such a system if using it as a desktop.
Some mainstream distros (e.g. Ubuntu) set their requirements higher than that.
The Linux kernel supports the 486 CPU (also used to support the 386, but it was dropped, although it's probably possible to restore it with some work - the 286 can't be easily supported because it lacks 32-bit registers).
If only this were the case. Common websites have become script ridden monstrosities that aggressively consume RAM and CPU. I routinely have 50+ tabs open; even on fairly recent hardware that can easily cause problems depending on which pages they contain.
opera did gracefully open 100+ tabs in 2005 on a dualcore with a gig of ram.
the key was and is: disable javascript
Meanwhile, FreeNAS worked and booted fine on it. Even though it only had 5GB ram. ;)