David Hannaford's robot pages.
Using a Microchip PIC processor and development environment
There are hundreds of PIC processors and a free software develpment environment (MPLAB) for writing code in several computer languages.
For a summary of the processor ranges have a look at the wikipedia article then follow this up with a vist to the Microchip site
Go here to download a copy of the MPLAB IDE V8 traditional development environment for use when writing in C or Assembler. You can also download the new Java Netbeans based environment MPLABX from here but note that as at May 2011 it was still a Beta version so may not be fully working or free of bugs yet.
I recommend starting with a microprocessor in a 28 or 40 pin DIP package device as it will be easier to try out on a breadboard or stripboard, than some of the very small SMD devices.
Something like the PIC18F2520 is a good one to start with for a line follower or other similar mobile robot as it has 2 PWM outputs, up to 10 analogue inputs, 32Kb of program memory, 1532 bytes of data memory and 256 bytes of EEPROM and will run at anything between 2 and 5.5 volts. There is a 28 pin version and a 40 pin version which has extra I/O ports. It can be run without an external crystal giving up to 8MIPS which should be fast enough for most initial experiments. Coding can be done in C or Assembler and there are many examples on the Microchip site or on the internet. The datasheet for this device is here. Pay particular attention to section 23 which tells you how to set the configuration bits which must be set correctly for the device to download programs correctly and run.
(More to be added here about datasheets, manuals and configuration bit setting) If you are going ahead before I complete this, take plenty of time reading the datsheet for your particular device and understand how to set the configuration bits.