The Project Akita OS (Orange OS) was started with the intent to design a lightweight operating system. It contains a small kernel designed for those interested in the low-level, practical aspects of building an x86 system. The host development environment is designed to work around the Bochs x86 emulator, so that you can easily test changes to the kernel.
blueflops is a two-floppy Linux distribution with a graphical Web browser (links) and an IRC client (rhapsody). The kernel has most of the Ethernet drivers compiled in as modules (including the PCMCIA ones) and PPP support (for dialup connections). The browser is linked with OpenSSL. The scripts are all accessible by a setup script and have a nice dialog frontend.
alcolix is a minimal Linux rescue distribution with the goals of being small, compatible, and very usable. It has a cozy shell and a multitude of partition rescue/editing tools, all based on up-to-date releases (e.g., 2.4.x kernel with USB support). It uses cpio.bz2 data disks and has a full GRUB bootloader, memtest86, and more.
Tunix is a set of tools used to generate small bootable Linux images. It can be used to learn how to roll your own distribution, or to port embedded systems. The basic release uses busybox and has a kernel with netfilter-enabled modules. A uclibc iptables binary is included, so you can roll your small firewall from a floppy.
G4L is a hard disk and partition imaging and cloning tool. The created images are optionally compressed, and they can be stored on a local hard drive or transferred to an anonymous FTP server. A drive can be cloned using the "Click'n'Clone" function. G4L supports file splitting if the local filesystem does not support writing files larger than 2GB. The included kernel supports ATA, serial-ATA, and SCSI drives. Common network cards are supported. It is packaged as a bootable CD image with an ncurses GUI for easy use.
NASLite is a Network Attached Storage (NAS) server operating system designed to transform a basic computer into a dedicated file server. Utilizing highly optimized versions of Samba, uCLibc, BusyBox, and various other Linux tools, it provides SMB/CIFS, FTP, or NFS filesystem support. It accommodates multiple client OSes: Windows, Mac OS X, and Linux. NASLite offers SMART disk monitoring and large file support, and is incredibly easy to install and administer.