Because of their small or non-existent footprint, micro-Linuxes are especially suited to run on laptops - particularly if you use a company-provided laptop running Microsoft-Windows9x/NT. Or for installation purposes using another non Linux machine. There are several micro Linux distributions out there that boot from one or two floppies or CD/DVD.
Knoppix by Klaus Knopper is a bootable CD with a collection of GNU/Linux software, automatic hardware detection, and support for many graphics cards, sound cards, SCSI and USB devices and other peripherals. KNOPPIX can be used as a Linux demo, educational CD, rescue system, or adapted and used as a platform for commercial software product demos. It is not necessary to install anything on a hard disk. Due to on-the-fly decompression, the CD can have up to 2 GB of executable software installed on it. A kix (Knoppix mini CD) is now available in the contrib directory.
MuLinux by Michele Andreoli.
tomsrbt "The most Linux on one floppy. (distribution or panic disk)." by Tom Oehser.
Trinux Trinux "A Linux Security Toolkit" by Matthew D. Franz.
hal91 hal91 is a very small Linux distribution that fits on one floppy disk. You need at least a 386 machine (FPU not necessary) with 8 mb ram to run HAL91. The entire system runs in ram, so you can remove the floppy after booting. The kernel supports IDE hard disks and ATAPI cdrom drives. Supported filesystems are ext2, iso9660 and vfat, optional encryption using AES is possible. Limited support for ethernet cards (NE2000 only) is also included. Support for scsi adapters, parallel zip drive and other ethernet cards is possible by loading kernel modules from an optional package.
floppyfw by Thomas Lundquist.
minilinux: Minimal linux package. UMSDOS filesystem (no repartition), TCP/IP and SLIP/PPP, X Windows including Xmosaic. Support Soundblaster, mouse, modem, SCSI.
Monkey Linux is a minimal Linux ELF distribution in 7.5MB archive (5 diskettes) designed to be used within MSDOS and to allow the user to experiment with Linux anywhere he/she wants.
DLX by Erich Boehm is a full featured linux system running on Intel PC's. The special thing is that DLX comes with only one 3,5" floppydisk. DLX boots with a kernel >= 1.3.89 and starts a ramdisk image. In addition to that DLX also has a writeable ext2 filesystem of about 130 kb on the same disk to easily store configuration scripts (survives booting, is not on the ramdisk !). Further is DLX fully prepared for the paralell-port ZIP-Drive which allows you to mount 100 mb disks. You can even put large programs like perl5 on the disk because a special directory on the ZIP-disk is mounted as /usr/local/*!
C-RAMDISK creates a bootable X Windows system that fits on two 1.44 MB floppies. The kernel (2.0.26) includes networking (PPP and dialin script, NE2000, 3C509) and the driver for the parallel port ZIP drive as modules. The file system contains pppd, rlogin, tar and ncftp and a small X Windows system. Requires a Linux system (with 2.0.0 kernel or above) to create the 2 floppies. The cramdisk floppy set will boot to "xdm" on a 486/pentium with 16MB RAM. For networking, the IP addresses and/or ppp dialin sequence need to be set. A method for modifying the floppy image is included.
SmallLinux by Steven Gibson. Three disk micro-distribution of Linux and utilities. Based on kernel 1.2.11. Root disk is ext2 format and has fdisk and mkfs.ext2 so that a harddisk install can be done. Useful to boot up on old machines with less than 4MB of RAM.
cLIeNUX by Rick Hohensee client-use-oriented Linux distribution
linux-lite by Paul Gortmaker for very small systems with less than 2MB RAM and 10MB harddisk space (1.x.x kernel)
You may also consider some of the boot floppies provided by various distributions falling into this category, e.g. the boot/rescue floppy of Debian/GNU Linux.
If you like to build your own flavour of a boot floppy you may do so manually, as described in the Boot-Disk-HOWTO or using some helper tools, for instance mkrboot (provided at least as a Debian/GNU Linux package) or pcinitrd, which is part of the PCMCIA-CS package by David Hinds.
Also you might try to build your Linux system on a ZIP drive. This is described in the ZIP-Install-HOWTO .