The PIC microcontrollers are one of the most popular 8-bit microcontrollers.
Microchip have hundreds of different microcontrollers from the tiny SOT23 package to 84-lead PLCC.
They can run up to 40 Mhz and execute instructions at four clock cycle.

PLUS:
They are cheap! The low end devices (PIC10Fxx) cost $0.40/ea in volume.
Free MPLAB development tool is available for programming in assembler. There are plenty of low cost development programmers etc.
Great chioce from many devices available with difference memory size and peripherials.
GPIO ports source 20mA and can drive direct LEDs etc.
The old OTP 'C' parts are one of most reliable controlers available on the market.
PICs are available in automotive temperature range -40+125C

MINUS:
Writing in Assembler is art of programming as there is no software stack, paging, GPIO read modify doesn't work.
Some new flash devices have hardware bugs and are not so reliable as old OTP devices.
No compatibility between different PICs and you have to re-write your code every time you move from one PIC to other.

The ARM microcontrollers are High-Performance, 16/32-Bit RISC Core devices. ARM market is one of the most fastest growing microcontroller market. The prices of ARM devices now are similar to 8-bit devices, while they are providing much more power and peripherials than any other 8-bit microcontroller do.
They are available from number of vendors like: Analog Devices, Atmel, Cirrus Logic, OKI, Philips Semiconductors, ST Microelectronics, Texas Instruments and many others (Intel, Freescale, Samsung, Sharp, Hynix, etc).
Many experts say that in the next 5 years ARMs are going to replace the industry standard 8051 architecture in almost all applications.

Olimex aim is to provide low cost development tools and boards for as many ARM vendors as possible, this year we'll cover all above 7 vendors and will have more than 40 different development boards for ARM7 and ARM9 device.

Few years ago to start with ARM developing the companies had to spend tenths of thousands of USD to buy compiler, debugger/emulator and development board, now everybody who want's to learn ARMs can start with under $100 budged buying JTAG + Development board and using the free ARM GCC C compiler.

PLUS:
Very fast: most ARM7 cores run at 60Mhz and ARM9 cores run at 150Mhz+ providing more power than old 386 Intel processors.
Low power: ARM7 cores need only approx 0.5-1mA per Mhz
Great range of peripherials: ADC, DAC, USB, SPI, UART, I2C, CAN, Ethernet, SDRAM.
Lot of internal Flash: 32KB-1MB, Lot of internal RAM: 4-256KB.

MINUS:
too complex to beginners, definitely this one should be not your 'first steps in microcontrollers' ;)

The MSP430 microcontrollers are Ultra-Low-Power mixed signal, 16-Bit RISC Core devics.
They an run up to 8Mhz (up to 16 Mhz for the new MSP430F2xxx series) and their consumption is only 250 uA per MIPS, which makes them perfect for portable and handheld devices.

PLUS:
Very low power: 250 uA per MIPS.
Mature product with very clean architecture - code porting between different members of MSP430 family needs alsmost no re-touch.
Avaliable in any quantity through TI distributors, with lots of application notes and code examples written.
Very good range of peripherials: Precise ADC and DACs, Comparators, OAMPs on chip, LCD drivers, SPI, UART, DMA.
The new members MSP430X have extended instruction set and allow more than 64KB memory addressing.

MINUS:
Von Neuman architecture, instructions take from 1 to 4 bytes, and are performed in 1 to 6 clocks.