The applications engineering group in DS produces example designs using the CPUs and support chipsets. These are typically PC-AT size motherboards, with all the functionality that you'd typically find on a high-end Pentium motherboard. Originally, these example designs were intended to be used as starting points for third-parties to produce motherboard designs from. These first-generation designs were called Evaluation Boards (EBs). As the amount of engineering required to build a motherboard has increased (due to higher-speed clocks and the need to meet RF emission and susceptibility regulations) the emphasis has shifted towards providing motherboards that are suitable for volume manufacture.
Digital's system groups have produced several generations of machines using Alpha processors. Some of these systems use support logic that is designed by the systems groups, and some use commodity chipsets from DS. In some cases, systems use a combination of both.
Various third-parties build systems using Alpha processors. Some of these companies design systems from scratch, and others use DS support chipsets, clone/modify DS example designs or simply package systems using build and tested boards from DS.
The EB64: Obsolete design using 21064 with memory controller implemented
using programmable logic. I/O provided by using programmable logic to interface
a 486 
- 
ISA bridge chip. On-board Ethernet, SuperI/O
(2S, 1P, FD), Ethernet and ISA. PC-AT size. Runs from standard PC power supply.
The EB64+: Uses 21064 or 21064A and APECs. Has ISA and PCI expansion (3 ISA, 2 PCI, one pair are on a shared slot). Supports 36-bit DRAM SIMs. ISA bus generated by Intel SaturnI/O PCI-ISA bridge. On-board SCSI (NCR 810 on PCI) Ethernet (Digital 21040), KBD, MOUSE (PS2 style), SuperI/O (2S, 1P, FD), RTC/NVRAM. Boot ROM is EPROM. PC-AT size. Runs from standard PC power supply.
The EB66: Uses 21066 or 21066A. I/O sub-system is identical to EB64+. Baby PC-AT size. Runs from standard PC power supply. The EB66 schematic was published as a marketing poster advertising the 21066 as ``the first microprocessor in the world with embedded PCI'' (for trivia fans: there are actually 2 versions of this poster - I drew the circuits and wrote the spiel for the first version, and some Americans mauled the spiel for the second version)
The EB164: Uses 21164 and ALCOR. Has ISA and PCI expansion (3 ISA slots, 2 64-bit PCI slots (one is shared with an ISA slot) and 2 32-bit PCI slots. Uses plus-in Bcache SIMMs. I/O sub-system provides SuperI/O (2S, 1P, FD), KBD, MOUSE (PS2 style), RTC/NVRAM. Boot ROM is Flash. PC-AT-sized motherboard. Requires power supply with 3.3V output.
The AlphaPC64 (aka Cabriolet): derived from EB64+ but now baby-AT with Flash boot ROM, no on-board SCSI or Ethernet. 3 ISA slots, 4 PCI slots (one pair are on a shared slot), uses plug-in Bcache SIMMs. Requires power supply with 3.3V output.
The AXPpci33 (aka NoName), is based on the EB66. This design is produced by Digital's Technical OEM (TOEM) group. It uses the 21066 processor running at 166MHz or 233MHz. It is a baby-AT size, and runs from a standard PC power supply. It has 5 ISA slots and 3 PCI slots (one pair are a shared slot). There are 2 versions, with either PS/2 or large DIN connectors for the keyboard.
Other 21066-based motherboards: most if not all other 21066-based motherboards on the market are also based on EB66 - there's really not many system options when designing a 21066 system, because all the control is done on-chip.
Multia (aka the Universal Desktop Box): This is a very compact pedestal desktop system based on the 21066. It includes 2 PCMCIA sockets, 21030 (TGA) graphics, 21040 Ethernet and NCR 810 SCSI disk along with floppy, 2 serial ports and a parallel port. It has limited expansion capability (one PCI slot) due to its compact size. (There is some restriction on when you can use the PCI slot, can't remember what) (Note that 21066A-based and Pentium-based Multia's are also available).
DEC PC 150 AXP (aka Jensen): This is a very old Digital system - one of the first-generation Alpha systems. It is only mentioned here because a number of these systems seem to be available on the second-hand market. The Jensen is a floor-standing tower system which used a 150MHz 21064 (later versions used faster CPUs but I'm not sure what speeds). It used programmable logic to interface a 486 EISA I/O bridge to the CPU.
Other 21064(A) systems: There are 3 or 4 motherboard designs around (I'm not including Digital systems here) and all the ones I know of are derived from the EB64+ design. These include:
Other 21164(A) systems: The only one I'm aware of that isn't simply an EB164 clone is a system made by DeskStation. That system is implemented using a memory and I/O controller proprietary to Desk Station. I don't know what their attitude towards Linux is.