The following distributions match your criteria:
1. Damn Small Linux
Damn Small Linux is a business card size (50MB) live CD Linux distribution. Despite its minuscule size it strives to have a functional and easy to use desktop. Damn Small Linux has a nearly complete desktop, including XMMS (MP3, and MPEG), FTP client, links-hacked web browser, spreadsheet, email, spellcheck (US English), a word-processor, three editors (Nedit, nVi, Zile [emacs clone]), Xpdf, Worker (file manager), Naim (AIM, ICQ, IRC), VNCviwer, SSH/SCP server and client, DHCP client, PPP, PPPoE, a web server, calculator, Fluxbox window manager, system monitoring apps, USB support, and soon it will have PCMCIA support as well. If you like Damn Small Linux you can install it on your hard drive. Because all the applications are small and light it makes a very good choice for older hardware.
2. Feather Linux
Feather Linux is a Linux distribution which runs completely off a CD or a USB pendrive and takes up under 128MB of space. It is a Knoppix remaster (based on Debian), and tries to include software which most people would use every day on their desktop.
3. Flash Linux
Flash Linux is a customised Linux distribution designed to be run directly off a USB key or other (similar) forms of bootable flash memory. It should work within the constraints of 256MB of (flash) memory although larger devices may also be used. Flash Linux is based on Gentoo Linux and new versions and bugfixes should track the stable Gentoo tree. Whereas Gentoo is a source distribution, Flash Linux is a binary-only distribution.
4. Flonix
Flonix USB Edition is a light-weight GNU/Linux operating system for personal computers, desktop-oriented. Flonix USB Edition run from USB key drives.
5. GentooTH Live CD/USB Linux
GentooTH Live CD/USB Linux is a Gentoo-based Russian/Ukrainian distribution designed to run from a CD or a USB storage device.
6. Knopperdisk
Knopperdisk is a Linux distribution designed for a USB pen drive. It is based on Gentoo Linux and contains various programs and utilities, such as network-related tools.
7. Puppy Linux
Yes, Puppy Linux is yet another Linux distribution. What's different here is that Puppy is extraordinarily small, yet quite full featured. Puppy boots into a 64MB ramdisk, and that's it, the whole caboodle runs in RAM. Unlike live CD distributions that have to keep pulling stuff off the CD, Puppy in its entirety loads into RAM. This means that all applications start in the blink of an eye and respond to user input instantly. Puppy Linux has the ability to boot off a flash card or any USB memory device, CDROM, Zip disk or LS/120/240 Superdisk, floppy disks, internal hard drive. It can even use a multisession formatted CD-R/DVD-R to save everything back to the CD/DVD with no hard drive required at all!
8. RUNT Linux
RUNT (ResNet USB Network Tester) is Slackware Linux designed to run from a 128MB USB pen drive. It consists of a boot floppy image and a zip file, similar to "zipslack". It is intended to be a fairly complete Linux installation for use as a testing tool capable of booting on any x86 computer with a USB port and a bootable floppy drive. The boot floppy is based on Slackware's bare kernel. It contains an initial ramdisk to load USB-storage related modules and it pauses for 5 seconds to allow the drive to initialize. The bootdisk also contains Memtest86, a very useful RAM testing tool, which can be started by typing memtest at the boot prompt. The zip file contains a UMSDOS filesystem designed to be extracted onto a 128MB pen drive with an MSDOS filesystem using 2K clusters.
9. Slax
Slax is a Slackware-based bootable CD containing a Linux operating system, designed with a modular approach. Despite its small size, Slax provides a wide collection of pre-installed software for daily use, including a well-organised graphical user interface and useful recovery tools for system administrators.
