I still run, and am writing this from, a 16-or-17 year old Dell E6510 (i5-540) that serves as my "around the house" computer. The battery life (with a huge 9 cell that protrudes out the back) isn't great, and it's hot and heavy, but with 8GiB of RAM and an SSD it works pretty well on Trixie with Cinnamon.

My main machine is a 13 year old Lenovo y510p running Debian and KDE. You'd be hard-pressed to tell that it's anywhere near that age.

The only aspect that has been annoying with both is graphics. Both machines are nvidia and are long past their support periods. The y510p has SLI (one graphics card is in the CD drive slot) which never worked on Linux. When removing the second card, the on-processor Intel graphics can be used, which have better support than nvidia, so I stick with that. I don't do anything graphics intensive anyway.

The biggest upgrade with old computers, without any doubt, is an SSD. I still remember getting my first one back in about 2011, a used 60GiB OCZ Vertex, and it was truly magic seeing the computer boot to the desktop in a few seconds even on a core 2 duo.