I remember staying up late (UK) at the Billenium (2:46 AM Sunday Sep 9th 2001), thinking that was bound to be the most newsworthy event of the week, watching the seconds tick past on a "while(sleep 1); do date" loop, with slashdot in one window, IRC in another, all running on an enlightenment window manager. 500M seconds later I was in Washington DC in a hotel, watching it tick up on an rxvt on my laptop, with HN in…
A former employer's telephony software had a 9-character intstring field for the Unix timestamp, so there was a bug when it rolled over to 1000000000 in 2001. Pretty rare, I think. Unix timestamps back then were usually 32-bit ints, so good until 2038. And hopefully they'll be 64 bits everywhere that matters well before 2038.
Almost all things that have a timestamp leave you in no doubt which 136-year period they were taken in. For those, 32 bits is plenty.