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).

I/O Boards
Arduino Uno - 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. It is similar to the Duemilanove, but has a different USB-to-serial chip the ATMega8U2, and newly designed labeling to make inputs and outputs easier to identify. 
Mega2560 - The version of the Mega released with the Uno, this version features the Atmega2560, which has twice the memory, and uses the ATMega 8U2 for USB-to-serial communication.
Nano - A compact board designed for breadboard use, the Nano connects to the computer using a USB Mini-B cable.
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.
Bluetooth - The Arduino BT contains a bluetooth module that allows for wireless communication and programming. It is compatible with Arduino shields.
Pro - This board is designed for advanced users who want to leave a board embedded in a project: it's cheaper than a Diecimila and easily powered by a battery, but requires additional components and assembly.
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.
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.
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.
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. (including Schematics and CAD Files)
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.

Shields
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.
XBee Shield - This shield allows multiple Arduino boards to communicate wirelessly over distances up to 100 feet (indoors) or 300 feet (outdoors) using the Maxstream Xbee Zigbee module.
Motor Shield - This shield allows an Arduino board to control DC motors and read encoders.
Ethernet Shield - This shield allows an Arduino board to connect to the internet.