Learning about microcontrollers
If you want to learn about microcontrollers, basically a single chip with a microprocessor (aka CPU), RAM, and program memory (ROM, EPROM, EEROM/EEPROM, or increasely common Flash memory) you can easily find many development kits to make it easy to get started. Some are even very cheap (~ $20-50 USD). The three most common microcontrollers for hobbists are the BASIC Stamp 2 modules from Parallax, the PIC series from Microchip, and the AVR series from Atmel.
If you don't have experience programming, then the most common processor to start with is the BASIC Stamp 2 modules that you can easily program in BASIC rather than having to learn a low level processor specific assembly language. With the BASIC Stamp 2 (BS2) you could get started with programming kits for $80-150 US which includes everything you need to get started programming a BS2 module.
Next is the PIC microcontrollers which are 8 and 16 bit RISC processors with a modifed Harvard architecture rather the more common von Newmann architecture that have a long history (from the 1970s). You can use the free MPLAB IDE for Windows to write programs, assemble, and debug in assembly. There are many various PIC programmers, a hardware device, available to load your program code from your PC to the PIC processors. Two (of many) affordable programmers are the Wisp628 (NL) or the Olimex made Tait style programmer from Spark Fun (US). To learn more about PIC microcontrollers you should check out the PIC List mailing list and its web site.
Two suggested PIC processors to get started with are the 16F84(A) and the 16F628(A) available in DIP (16F628-20/P and 16F84A-20/P) and surface mount packaging. Glitchbuster is one of several source for PICs. Other common suppliers include Mouser, Jameco, and Digikey in US and Canada.
The third most common microcontroller for hobbyists is Atmel 8-bit RISC AVR that is simple but has very good performance. The free Windows AVR Studio includes an assembler and simulator. For programming the devices you can use the AVR ISP In-System Programmer for $34 USD. There is also the cheap but fun AVR Butterfly demo board, available for $20 USD from Digikey (ATAVRBFLY-ND). The best web resource for AVR information for hobbyists is AVR Freaks.
There are open source development tools for Linux (and DOS/Windows) to program the PIC and AVR in assembly and high level languages such as JAL and C. Most of these can be found on SourceForge.
Addendum: An excellent and free tutorial about PIC microchips is called Elmer 160. It is available online from AmQRP, and is written by John McDonough, WB8RCR.