I love PLD Rescue, for any quick task where I need a text mode linux that runs anywhere. (even can boot from network)
once booted you're logged on as root on six tty, and you have access to lots of various disk and network tools (including the obvious ones : ssh, scp, fdisk, sshfs, dd, dd_rescue etc.)
PLD is also its own distro, which claims to be simple (the distro itself, not thg' ease of use) but I didn't run it. you have an i486 and an i686 version for instance.
else I do mostly debian and ubuntu. ubuntu can be used in the same exact way as debian, i.e. installing it text mode and adding a few packages. can fit on a 96MB computer if you're going to run abiword and card games and the like. (or even vlc and music player)
interesting is the dillo browser, I ran it many years ago when it was 1.x version, it has few features but is insanely fast.
for a while it was marred in a 2.x version running on an experimental toolkit (fltk 2.0) so it wasn't published in distros, but lately there's the 3.x version running on the new fltk 1.3, I hope it's in ubuntu 12.04 and debian 7 (dunno), will get in newer versions of tiny distros no doubt.