Counting only my primary desktop distro and skipping personal/work servers or experimental installs my history is like this:
Slackware -> RedHat -> SuSE -> Debian -> Gentoo -> Ubuntu -> Mint
I, like many in the thread, started with Slack back in the "box full of floppies" era. We generally would have install parties at the offices of
the ISP my buddies owned so real internet could be used instead of interminable disk swapping or (even worse) dial-up. Fun times were had.
Upgrading that system, by hand, from a.out to ELF without completely hosing it was a great adventure!
Currently I'm running Mint 12 on my desktop, Mint 13 on my laptop, and Debian Squeeze on my home file/DHCP/etc. server.