PC

Several open hardware project that are building something with most of the functionality of a standard desktop PC:

Motherboards that run Linux, including
 * ARMUS Embedded Linux Board
 * Linuxstamp
 * the Kestrel
 * Balloon Xscale ARM+FPGA dev board
 * Computer Components wiki: Custom Notebook
 * the OpenBook project is an open source hardware and software project designing a computer tablet ... Everyone can contribute and help to shape the OpenBook hardware and software specifications on the OpenBook Project website. See the Openbook wiki (http://obook.info/)
 * wikibooks: build a laptop has a few tips on a semi-custom notebook computer (but it doesn't have enough flexibility to, say, make one with a RAID1 mirroring).

Boards that don't run Linux (yet), including
 * Many of the "TTL CPUs" listed in | Wikibooks: Microprocessor Design are more-or-less open hardware. Several of them have video output and keyboard input connectors.
 * Several of the Parallax Propeller Development Boards are more-or-less open hardware. Many of them have VGA output and keyboard and mouse input connectors.
 * "The Maximite is a small and versatile computer running a full featured BASIC interpreter with 128K of working memory. It will work with a standard VGA monitor and PC compatible keyboard and because the Maximite has its own built in SD memory card and BASIC language you need nothing more to start writing and running BASIC programs. The design is free and open source including the software and BASIC interpreter." The "haiqu" has ported BSD to the Maximite and UBW32. Apparently (?) also supports Arduino shields.
 * "Special Computing" has a list of SBCs and accessories -- BeagleBoard, IGEPv2, HawkBoard, etc. -- Can any of them run Linux?

Many of the other open circuits projects are designed to plug into a standard desktop or laptop PC.

Novena
Bunnie is building Novena, an open laptop motherboard.
 * "Building my Own Laptop": "all the design documentation is open, so others of sufficient skill and resources can also build it. The hardware and its sub-components are picked so as to make this the most practically open hardware laptop I could create using state of the art technology. You can download, without NDA, the datasheets for all the components, and key peripheral options are available so it’s possible to build a complete firmware from source with no opaque blobs."
 * "Update on Our Laptop (aka Novena)": "All our progress has been publicly trackable via our git repos and on our wiki. There’s also a discussion forum"
 * "Posts Tagged 'novena'".

EOMA68 Libre Laptop
"Funnily enough, the creation of a 15.6in eco-conscious Libre Laptop is exactly what I have been working on for just over a year, now. The keyboard is implemented using an STM32F072 with 8×16 matrix scanning. the processor, memory and storage is on a separate removable module, a standard created specifically for the purpose, known as EOMA68. There are two CPU Cards in active development: one is EOMA68-A20, the other is EOMA68-jz4775. The first is a dual-core 1.2ghz ARM Cortex A7 (the A20 from Allwinner), the second is entirely FSF-Endorseable: an Ingenic 1.2ghz MIPS processor called the jz4775. The source code for the casework is GPLv2 and is available *right now* for anyone to 3D-print their own laptop case or adopt it for any other project. The source code for the STM32F072 firmware is GPLv2, uses libopencm3, and is again available *right now*. If you’re interested you can follow the projects here: http://rhombus-tech.net/community_ideas/laptop_15in/news http://rhombus-tech.net/allwinner_a10/news/ http://rhombus-tech.net/ingenic/jz4775/news and if you’d like to sign up for the upcoming crowd-funding you can do so here: https://www.crowdsupply.com/eoma68" -- g2-48364b13e4baeb7cc5743f5780761309 http://hackaday.com/2016/01/13/stallmans-one-mistake/#comment-2884397


 * EOMA68 news
 * "EOMA68 Libre Laptop features upgradeable CPU card".
 * "Embedded Open Modular Architecture/EOMA-68": the EOMA-68 Specification
 * http://rhombus-tech.net/
 * a git repository for EOMA-compliant Open Hardware Devices
 * EOMA-68 discussion thread at the element 14 forum
 * articles tagged "EOMA-68" at liliputing
 * "Improv is a $75 modular, ARM-based computer core (EOMA-68)"
 * "EOMA-68: The Return" by Paul Boddie at FSFE
 * a hand-held EOMA-68 games console

Pi Laptop
The Pi-Top enclosures hold the Raspberry Pi and a LCD panel in an approximation of a laptop computer.