Which devices are similar to Arduino boards? Please only list devices / competitors that are comparable in terms of hardware.
I see "Arduino" becoming a metonym for user-friendly embedded development platforms.
A more accurate description is synechdoche, example: Kleenex. I like this question & wish I could have asked this early on in my Arduino development! Because I see Arduino as a synechdote, this could lead to too broad of an answer, but I will try giving a highlights kind of answer.
There is a Wiki List of Arduino boards and compatible systems which I just read and like enough I may need to figure out how to contribute & edit wikis.
Aspects of the question I'll try to answer:
1) architecture which could be a synonym for processor type.
2) pin locations aka the all important pinouts.
3) developer environment how to make it work.
4) offshoots where things get very interesting.
"Arduinos" are based on AVR processors. There are a couple variants, easy to research.
AVR ATmega based processors, which Arduino initiated from.
Netduino and its myriad of offshoots. These have more RAM and clock speed.
ChipKIT and others in the Non ATMega section of the wiki, usually with more RAM and clock speed.
Entirely different embedded platforms Like raspberry PI, beagle, etc.
This is the physical interface to the processor and I believe the heart of most problems I read about while researching my own projects. Sadly, I couldn't even say what pins do what, as I never use "stock" Arduino boards anymore.
Pin function is what matters and should be the name of this part. Don't obsess on the pin number. Each pin can have multiple uses. This is rooted from embedded design needing to be as compact as possible while maximizing usefulness. These amazing pinout graphics help illustrate.
The Arduino IDE (based on processing) is the supported default way to compile code and upload into Arduinos. To help deal with the synechdoche-ism of Arduino, Majenko created UECIDE to allow one place to program and delpoy to all your "Arduino boards" regardless of architecture.
If you google AVR freaks, you learn this can be done via the command line, too.
The NETduino and other NET platforms use Microsoft's "dot NET" tools to program the platform. The methodology behind this is a bit different and rubs classical embedded engineers the wrong way. The .NET platforms require compiled host software on the board. The modules in your Visual environment must have a matching version. Your code gets compiled into platform independent .NET objects, which then get downloaded to then interpreted on the platform. People making NET based boards are usually good about explaining the tool chain and development process.
Here's where user-friendly embedded design really shines. People love the Arduino and want mostly the same thing but with some mods or "improvements".
Ruggedino is one that an electrical engineer has electrically hardened the original design to better resist common user mistakes which could damage the AVR processor.
Freeduino has a model called the eleven which comes with a prototype area on the board so it's easy to use custom circuits in your sketches. This brand also believes in gold contacts, which suffer heat saturation better than the way original Arduinos are made.
Seeedstudio (with 3 es) is great because they make a Mega that has Uno pinout, so you get more RAM. And their PCBs are red.
ChipKIT platform get my love for maintaining Arduino pinout faithfully while bringing a processor with incredible resources to our universe. They give us these extra pins by having two row headers. They add another host of pins on the inside of the standard pins. This (and 32K of RAM) helped me greatly with my ambitious project.
Updated Sep 2015:
An impressive and nearly comprehensive list of development boards can be found via this search on Mouser. There are offerings far more powerful than an Arduino for less than $10. The trade off is they all have different I/O pins with different capabilities and specifications. And each one's MCU specs will need to be critiqued for exactly which functions come with each different product.
The Cypress CY8KIT-059 for $9 has their "PSoC5" architecture, which means generic blocks are programmable (like FPGAs) via their IDE. They can make Op Amps, comparators, CAN controllers, all sorts of craziness. Note that their $4 dev board the -049 is less newbie friendly in how it downloads code to the target; totally worth the extra $5 for the -059's built in FTDI-like capability.