x86

Domainatrix
Assembly language OS for x86 architecture, hot-swappable kernel, made to serve the Web, written originally for programmer's personal interest and education after moving to the PC platform from his old 8-bit machine. Philosophically similar to V2 OS.
http://domainatrix.freeservers.com/

Hactar
Claims: all new, no equivalent design in extant OSs, an adventure into something really different, an answer to a What if? Runs on 386+, system disk is floppy, kernel size 32Kb; manages 4Gb RAM, 2Gb disk; semi-multitasking; unusual interface. [Open Source, WTOF PL]
http://anywherebb.com/hactar.html

HanoiOS
Self booting x86 OS implementation of Towers of Hanoi puzzle, very simple bootstrap loader and kernel; boots, presents shell-like prompt for valid integer input, used by kernel as count of disks to solve, prints list of moves.
http://www.kernelthread.com/hanoi/html/tos-x86.html

The Mobius: SourceForge
A few screenshots, details, links.
http://mobius.sourceforge.net/

PM_SZ_OS
Protected mode, 32-bit OS for i486 CPUs and up, full network stack, supports several filesystems, paging, deferred procedure call support, and virtual multiple screens with different resolution and scrollback. Free download.
http://www.geocities.com/the_real_sz/

RDOS
Multi-process/threaded protected mode OS for all i386+ systems, written in all 16-/32-bit Assembly in TASM, fully PROMable so can port to embedded systems with no keyboard and/or screen, stable and secure via segment protection and paging. [Open Source, GPL]
http://www.rdos.net/

ScottsNewOS
Runs on i386+ compatible, working GUI even on 4 MB. Coded in Assembly, C. Brief description, download link. [Open Source, GPL]
http://scottsnewos.sourceforge.net/

Synapse Operating Services
Protected mode, multitasking support, 32-bit; developed on x86-32, intended to run on x86-64 with some changes; DOS-like, but not fully compatible, use: to run ported DOS programs up to 512K. At SourceForge. [Open Source, BSD]
http://sourceforge.net/projects/comos/

TriangleOS
32-bit multitasking, multithreaded OS for x86 386+ CPUs, with GUI, FSs, applications, drivers, all in active development. Site has information, news, documents, screenshots, downloadable releases.
http://members.chello.nl/w.cools/

Visopsys
VISual OPerating SYStem: small, fast, home-brewed, open source OS kernel for x86. Includes project background, screenshots, source code and useful links for OS developers. [Open Source, GPL]
http://www.visopsys.org/

XAOS
Runs on i386+, 16-bit real mode, FAT12/16/32 (read-only, LFN support), coded in C++; downloads: binaries, source, utilities, game (tetris source); downloads. [Open Source]
http://www.mirzoyan.com/xaos/