Arch Linux is an i686-optimized Linux distribution. It is lightweight and contains the latest stable versions of software. Packages are in .tar.gz format and are tracked by a package manager that is designed to allow easy package upgrades. Arch is quite streamlined compared to some other distributions. Things that are relatively unused are not kept (info pages, for example). A default Arch install leaves you with a solid base; from there, you can add packages to create the custom installation you're looking for. Arch has a package build system that allows you to easily create your own packages, which makes it very easy to rebuild a package with your own custom configuration. Arch also aims to use the newer features available to Linux users, such as reiserfs/ext3 and devfs.
The Auditor security collection is a live-system based on KNOPPIX. It provides tools for analyzing the security of a system. It features a menu structure that reflects the stages of a security check: foot-printing, analysis, scanning, wireless, brute-forcing, cracking. In addition to about 300 security tools, the collection includes background information regarding standard configuration and passwords, truly extensive word lists, and more mundane productivity tools.
BG-Rescue Linux is a Busybox and uClibc-based rescue system with a 2.4 series Linux kernel. It supports full read/write support for NTFS using ntfs-3g. It is loaded from two floppy disks, a bootable CD-Rom, or a USB Stick. The system runs entirely in RAM. It supports a wide range of hardware (including SATA and DM/LVM2) and filesystems (including ext2/3, hfs/hfs+, and xfs) and can serve as a full backup/restore system for MS Windows systems which use FAT12/16/32 or NTFS. It also includes many utilities, including strong compresstion tools like lrzip. Automatic loading of the antivirus-program F-Prot from cdrom or usbstick is supported.
BG-Tiny Linux Bootdisk is a Linux bootdisk that does not use a ramdisk, so it will run on computers with very little RAM. It is basically a somewhat extended fork of Tiny Linux Bootdisk. It is based on Linux 2.4 series, uClibc, and BusyBox. It includes dosfsprogs, e2fsprogs, gpart, lilo, and ms-sys. Supported filesystems are ext2, ext3, iso9660, tmpfs, and vfat.
BLAG is a single-CD Linux distribution that has a suite of graphics, Internet, audio, video, office, and peer-to-peer file sharing applications. It is based on Fedora Core, Dag, Freshrpms, etc. It is up-to-date with all Fedora errata updates at the time of release, and uses apt/synaptic for easy upgrades and installation of new applications.
BeatrIX Linux is a 180-megabyte live CD that is also installable to hard drive. It features kernel 2.6.7, Gnome 2.8, Evolution 2.0, Firefox 1.0 with AdBlock, Open Office 1.1.2, Vim, Apt, xPDF and more. It tracks the Ubuntu package repository. It was originally built for the mini-ITX motherboards from Via, but it runs on just about any Pentium-class PC with 64 megs of RAM or more. It's a get-the-job-done distribution for people who want the basics.