There are multiple versions of the Arduino board. The current basic board, the Duemilanove, uses the Atmel ATmega328 (datasheet). The older Diecimila, and the first run of Duemilanoves used the Atmel ATmega168 (datasheet), while older boards use the ATmega8 (datasheet). The Arduino Mega is based on the ATmega1280 (datasheet).
Note: The reference designs for arduino are distributed under a Creative Commons license Attribution-ShareAlike 2.5. See So you want to make an Arduino? for more information and guidelines on producing your own hardware.
Duemilanove - This is the latest revision of the basic Arduino USB board. It connects to the computer with a standard USB cable and contains everything else you need to program and use the board. It can be extended with a variety of shields: custom daughter-boards with specific features.
Nano - A compact board designed for breadboard use, the Nano connects to the computer using a USB Mini-B cable.
Mega - A larger, more powerful Arduino board, shield compatible with the Duemilanove and Diecmila.
Bluetooth - The Arduino BT contains a bluetooth module that allows for wireless communication and programming. It is compatible with Arduino shields.
Mini - This is the smallest Arduino board. It works well in a breadboard or for applications in which space is at a premium. It connects to the computer using the Mini USB Adapter.
Mini USB Adapter - This board converts a USB connection into 5 volt, GND, TX and RX lines that you can connect to the Arduino Mini or other microcontroller.
LilyPad - Designed for wearable application, this board can be sewn onto fabric, and is a stylish purple.
Fio - Designed for wireless applications. It includes a socket for an XBee radio, a connector for a LiPo battery, and integrated battery charging circuitry. details
Pro - This board is designed for advanced users who want to leave a board embedded in a project: it's cheaper than a Duemilanove and easily powered by a battery, but requires additional components and assembly.
Pro Mini - Like the Pro, the Pro Mini is designed for advanced users requiring a low-cost, small board and willing to do some extra work.
Serial - It's a basic board that uses RS232 as an interface to a computer for programming or communication. This board is easy to assemble even as a learning exercise.
Serial Single Sided - This board is designed to be etched and assembled by hand. It is slightly larger than the Diecimila, but still shield compatible.
The hardware index lists all the Arduino boards made and the differences between them.
Shields are boards to be mounted on top of the Arduino board and that extend the functionality of Arduino to control different devices, acquire data, etc.
Products from others that we've tried and liked; compatible with the Arduino software.
Also check out the community-maintained list of related hardware on the playground.